distance problems (d=rt)
Post on 05-Jan-2016
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# 1.
(a.) How many “30 minute increments” are in 1 hour?
(b.) If someone traveled 20 miles in 30 minutes, then how many miles did they
travel in one hour?
(c.) If someone traveled 4 miles in 30 minutes, then how many miles did they
travel in one hour?
2min30
min60
20 • 2 = 40 miles
4 • 2 = 8 miles
# 2.
(a.) How many “20 minute increments” are in 1 hour?
(b.) If someone traveled 15 miles in 20 minutes, then how many miles did they
travel in one hour?
3min20
min60
15 • 3 = 45 miles
# 3.
If someone traveled 10 miles in 12 minutes, then how many miles did
they travel in one hour?
Number of 12 minute increments
in an hour:
5min12
min60
10 • 5 = 50 miles
# 4.
(a.) If 1,760 yards = 1 mile, then how many miles is 7040 yards?
(b.) How many miles is 5,280 yards?
yds
mileyds
1760
1
1
7040miles
1760
7040
4 miles
yds
mileyds
1760
1
1
5280miles
1760
5280
3 miles
# 5.
If 5,280 ft are in one mile, then how many miles is 10,560 feet?
ft
mileft
5280
1
1
10560miles
5280
10560
2 miles
# 6.
Fill in the chart for miles per hour. (1,760 yards = 1 mile and 5,280 feet =
1 mile)Distance Distance
in milesTime Total
increments in an hour
Miles per Hour
17,600 yards
10 miles 20 minutes
3 10•3 =30 miles/hr
5 miles 30 minutes
6 miles 40 minutes
3520 yards
30 minutes
15,840 feet
20 minutes
5 miles
2 5 • 2 = 10 mph6
miles
3/26 • (3/2) = 9 mph
3520/1760 =
2 miles 2 2 • 2 = 4 mph
15840/5280 =
3 miles3 3 • 3 =
9 mph
# 7.
Jack walked 2 miles in 30 minutes. Jane walked 1,760 yards in 12
minutes. In miles per hour, how much faster did Jane walk than Jack? (1760
yards = 1 mile)There are 2 “30-minute” increments in an hour and 5 “12-minute increments
in an hour.Jack walked 2 miles • 2 = 4
mphJane walked 1 mile • 5 = 5
mphJane walked 5 mph – 4 mph = 1 mph
faster
# 8.
Juan ran 1 mile in 6 minutes. Estelle ran 15,840 feet in 30 minutes. In
miles per hour, how much faster did Juan run than Estelle?
There are 10 “6-minute” increments in an hour and 2 “30-minute increments
in an hour.Juan ran 1 mile • 10 = 10
mphEstelle ran 15840/5280 miles • 2 = 3 miles •
2 = 6 mph
Juan ran 10 mph – 6 mph = 4 mph faster
# 9.
Sebastian walked 1 mile in 12 minutes. Julie walked 5,280 yards in 20 minutes. They both walked for 2 hours. How much further had Julie
walked than Sebastian? (1,760 yards = 1 mile)
There are 5 “12-minute” increments in an hour and 3 “20-minute increments
in an hour.Sebastian walked 1 mile • 5 = 5
mph
Julie walked 5280/1760 miles • 3 = 3 miles • 3 = 9 mph
Sebastian walked 5 • 2 = 10 miles in 2 hours.
Julie walked 9 • 2 = 18 miles in 2 hours.
Julie walked 18 – 10 = 8 miles further.
# 10.
John and Katie started at the same point. Katie walked 100 ft per minute. John
started 3 minutes after her and walked 150 ft per minute.
(a.) Make a table that shows how far Katie walked for each minute.
Min.0
1
Dist.0
100
(b.) Make a table that shows how far John walked for each minute. (He did not go
anywhere for the first 3 min.)Min.0
1 2 3 4
Dist.0
150
2
200
3
300
4
400
5
500
6
600
7
700
8
800
9
900
5
300
6
450
7
600
8
750
9
900
# 10.KATIEMin.0
1
Dist.0
100
(c.) How far had Katie walked before John caught her?
Min.0
1 2 3 4
Dist.0
150
JOHN
2
200
3
300
4
400
5
500
6
600
7
700
8
800
9
900
5
300
6
450
7
600
8
750
9
900
600
# 10.
(d.) The two equations: d = 100 t and
d = 150(t – 3) represent John and Katie’s distance. Which one
represents John? Explain why.
d = 150(t – 3)
He started later and had not walked as long as Katie.
# 10.(e.) Set the two equations, (d = 100
t and d = 150 (t – 3), equal to each other
and solve. How long had they walked before they had walked the
same distance?100 t = 150 (t – 3) 100 t = 150 t – 450 - 50 t = – 450 t = 9
# 10.(f.) What is the same distance that
they had walked?
100 (9) = 900 feet
# 10.(g.) Suppose that John had started
5 minutes later. What would his equation be?
d = 150(t – 5)
# 11.
Jackson and Tom started at the same place. Jackson walked 9 ft. per second.
Tom waited three seconds later and walked 12 ft. per second.(a.) Make a dual table that shows how far each
walked after each second.Time 0 1 2 3 4 5 6 7 8Jackson
Tom
(b.) How far had they walked before they had walked the same distance?
(c.) Solve the problem algebraically. Show supporting work.
9 18 27 36 45 54 63 72
12 24 36 48 60
9 (12) = 108
9 t = 12 (t – 3)9 t = 12 t – 36
- 3 t = - 36 t = 12
# 12.
Hiroshi and Juan both rode their scooters. Hiroshi started first and
rode 20 mph. Jack started 30 minutes later and rode 25 mph. How far had they traveled before
they had caught up with each other?
9 t = 12 (t – .5)9 t = 12 t – 6 - 3 t = – 6 t = 2
9 • 2 = 18 miles
# 13.
Distance = Speed • Time (or Rate • Time) d = r
tBrady rides his bicycle 10 miles at 15 miles per hour. How long did it
take him?
d = r t
d/r = t
10/15 = t = 2/3 hour = 40 minutes
# 14.
d = r tAaron, Bill, Colby, and Dillon all started at the
same place and same time and are going to the same place. Who is the closest person to their
destination? Who is the closest to their starting point?
Person Speed Time
Aaron 50 mph 3 hours
Bill 60 mph 2.5 hours
Colby 40 mph 4 hours
Dillon 55 mph 2 hours and 30 min
d = r t150 mi150 mi80 mi
137.5 miAaron and Bill are closest to
destination.Colby is closest to starting point.
# 15.
d = r tJulie and Tom rode their
bicycles to the same place. Julie rode 15 miles per hour and
it took her 1.5 hours. If Tom rode 12 miles per hour, how
long did it take him?Julie:
d = 15 • 1.5 = 22.5 miles
Tom:
12 • x = 22.5 miles
x = 22.5 / 12 = 1.875 hours
# 16.
Person Distance Time
Edgar 100 miles
1.25 hours
Frank 120 miles
2 hours
George 200 miles
200 minutes
Helen 150 miles
1 hour and 30 min
d = r tEdgar, Frank, George, and Helen
drove the following distances and times. Who was the fastest? Who
was the slowest?r = d/t80 mph60 mph60mph100 mph
Helen was the fastest.Frank and George were the slowest.
# 17.
d = r tFrom the same starting point,
Jane drove north at 50 mph for 3 hours and Tom drove east at 40 mph for 4 hours. How far are they directly apart from
each other?Jane:
50 • 3 = 150 miles
Tom:
40 • 4 = 160 miles
They are 150 + 160 = 310 miles apart.
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