variables on both sides story problems

VARIABLES ON BOTH SIDES

STORY PROBLEMS

“THE TOUGH STUFF”

A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?

Cost for Rent-a-wreck = 60 + .2m

A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?

Cost for Rent-a-wreck = 60 + .2m Cost for Lemon Leasers = 30 + .5m

A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?

Cost for Rent-a-wreck = 60 + .2m Cost for Lemon Leasers = 30 + .5m Set the two equal to each other

A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?

Cost for Rent-a-wreck = 60 + .2m Cost for Lemon Leasers = 30 + .5m Set the two equal to each other 60 + .2m = 30 + .5m

A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

This is a “same direction” problem.

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

This is a “same direction” problem. When going the same direction, the

distances are equal.

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

This is a “same direction” problem. When going the same direction, the

distances are equal. Use the formula d = rt

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time Distance

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoeJane

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe 6Jane

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe 6Jane 8

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe 6 tJane 8

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe 6 tJane 8 t - 15

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe 6 t 6tJane 8 t - 15

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe 6 t 6tJane 8 t - 15 8(t – 15)

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Set the distances equal to each other and solve.

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Set the distances equal to each other and solve.

6 𝑡=8(𝑡−15)

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Set the distances equal to each other and solve.

6 𝑡=8(𝑡−15)6 𝑡=8𝑡−120

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Set the distances equal to each other and solve.

6 𝑡=8(𝑡−15)6 𝑡=8𝑡−120−2 𝑡=−120

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Set the distances equal to each other and solve.

6 𝑡=8(𝑡−15)6 𝑡=8𝑡−120−2 𝑡=−120𝑡=60

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe 6 t 6tJane 8 t - 15 8(t – 15)

The t solved for was the time that JOE was on the road.

Jane’s time was (t – 15), or 45 minutes.

Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

Rate Time DistanceJoe 6 t 6tJane 8 t - 15 8(t – 15)

**BE SURE TO ANSWER THE QUESTION ASKED.

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

WillWayne

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50Wayne

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50Wayne 70

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 tWayne 70

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 tWayne 70 t - 2

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 6:00 amWayne 70 t - 2

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 6:00 amWayne 70 t - 2 8:00 am

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 8:00 am

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

50 𝑡=70(𝑡−2)

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

50 𝑡=70(𝑡−2)50 𝑡=70 𝑡−140

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

50 𝑡=70(𝑡−2)50 𝑡=70 𝑡−140−20 𝑡=−140

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

50 𝑡=70(𝑡−2)50 𝑡=70 𝑡−140−20 𝑡=−140𝑡=7h𝑟𝑠

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

Is 7 hours the answer to the question??

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

Is 7 hours the answer to the question??

This question asked for “what time”. That means the actual clock time.

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

Since t was the time for Will, add 7 hours to his departure time.

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

Since t was the time for Will, add 7 hours to his departure time.Will left at 6:00 am. Wayne catches him 7 hours later, or at 1:00 pm

Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

Rate Time Distance

Clock

Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am

Since t was the time for Will, add 7 hours to his departure time.Will left at 6:00 am. Wayne catches him 7 hours later, or at 1:00 pm**Be sure to include the proper am vs. pm designation

7-5: 17, 28, 33, 35 - 40

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