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STORY PROBLEMS II THE “REALLY TOUGH STUFF”

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STORY PROBLEMS II. THE “REALLY TOUGH STUFF”. General Directions for d = rt problems. Read the problem carefully. Ask yourself, “What am I trying to find.” Determine what kind of a problem it is. Write your equation and solve Ask yourself, “Did I answer the question asked?”. - PowerPoint PPT Presentation

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Page 1: STORY PROBLEMS II

STORY PROBLEMS II

THE “REALLY TOUGH STUFF”

Page 2: STORY PROBLEMS II

General Directions for d = rt problems

1. Read the problem carefully.2. Ask yourself, “What am I trying to

find.”3. Determine what kind of a problem

it is.4. Write your equation and solve5. Ask yourself, “Did I answer the

question asked?”

Page 3: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? What am I trying to find?How long does it take the MOTORBOAT to catch the canoe. In other words, how long is the motorboat on the water?

Page 4: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? This problem contains speed (rate) and

time.

Page 5: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? Use d = rt Make a table of the information.

Page 6: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoeMotorboat

Page 7: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12Motorboat

Page 8: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12Motorboat 21

Page 9: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12 tMotorboat 21

Page 10: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12 tMotorboat 21 t - 2

Page 11: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12 t 12tMotorboat 21 t - 2

Page 12: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12 t 12tMotorboat 21 t - 2 21(t - 2)

Page 13: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? The motorboat has caught the canoe

(same direction) The distances traveled by both must be

the same. Set the two distances equal to each

other and solve.

Page 14: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21(𝑡−2)

Page 15: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21(𝑡−2)

12 𝑡=21𝑡−42

Page 16: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21(𝑡−2)

12 𝑡=21𝑡−42−9𝑡=−42

Page 17: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21(𝑡−2)

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9

Page 18: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

)

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9 =4.6

Page 19: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

)

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9 =4.6

You can convert your answer to hours and minutes if you like.

Page 20: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21¿

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9 =4.6

You can convert your answer to hours and minutes if you like.The time you have found is the time for the canoe. You were not asked to find that. Find the motorboat’s time.

Page 21: STORY PROBLEMS II

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21¿

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9 =4 .6It takes the motorboat 2 hours and 40 minutes to catch the canoe. Or you can just leave it hours.

You can convert your answer to hours and minutes if you like.The time you have found is the time for the canoe. You were not asked to find that. Find the motorboat’s time.

Page 22: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4 km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you arrive at the top of the hill? This problem contains rate and time

(but it is given as “clock” time.) If you go to a location, then come

back, you have a “round trip” situation

In a round trip, the distances are equal.

Page 23: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? Make a table. Add a column for the “clock” time.

Page 24: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

UpDown

Page 25: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4Down

Page 26: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4Down 6

Page 27: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 tDown 6

Page 28: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 tDown 6 3 - t

Page 29: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 t 4tDown 6 3 - t

Page 30: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 t 4tDown 6 3 - t 6(3 – t)

Page 31: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 t 4t 9:00 amDown 6 3 - t 6(3 – t)

Page 32: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 t 4t 9:00 amDown 6 3 - t 6(3 – t) ????

Page 33: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)

Page 34: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡

Page 35: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

Page 36: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

𝑡=1810

Page 37: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

𝑡= 1810=1.8hours

Page 38: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

𝑡= 1810=1.8hours

This does NOT answer the question asked. This is how long it takes to get to the top of the hill, not AT WHAT TIME?

Page 39: STORY PROBLEMS II

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

𝑡=1810=1.4 hours

This does NOT answer the question asked. This is how long it takes to get to the top of the hill, not AT WHAT TIME?

If you left at 9:00 am, and it took 1.8 hours (or 1 hour 48 minutes), then you arrived at the top of the hill at 10:48 am.

Page 40: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the jets are 1250 miles apart. Find the speed of each jet.

The jets are flying in “opposite directions.”

To solve an opposite direction problem, ADD the distances traveled to find the distance apart.

Page 41: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Make a table.

Page 42: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestboundEastbound

Page 43: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25Eastbound

Page 44: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25Eastbound r

Page 45: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2Eastbound r

Page 46: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2Eastbound r 2

Page 47: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2

Page 48: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

Page 49: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

Page 50: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=1250

Page 51: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=12504𝑟+50=1250

Page 52: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=12504𝑟+50=1250

4𝑟=1200

Page 53: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r + 25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=12504𝑟+50=1250

4𝑟=1200𝑟=300

Page 54: STORY PROBLEMS II

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r +25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=12504𝑟+50=1250

4𝑟=1200𝑟=300

The rate (r) is the rate of the eastbound jet. Therefore, the westbound jet is flying at 325 mph.

Page 55: STORY PROBLEMS II

Wrap-up There are three type of problems. Same direction Round-trip Opposite direction In same direction and round-trip

problems, you set the distances equal to each other.

In opposite direction, you add the distances together.

Page 56: STORY PROBLEMS II

Assignment2.5B: 10 - 24