DISTANCE PROBLEMS (d=rt)

# 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?

2min30min60

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?

3min20min60

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:

5min12min60

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

mileyds17601

17040

miles17607040

4 miles

yds

mileyds17601

15280

miles17605280

3 miles

# 5.

If 5,280 ft are in one mile, then how many miles is 10,560 feet?

ft

mileft52801

110560

miles528010560

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

miles3/2

6 • (3/2) = 9 mph

3520/1760 =2 miles 2 2 • 2 =

4 mph15840/5280 =3 miles 3 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 mph

Jane 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

1Dist.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 4Dist.0

150

2

200

3

300

4

400

5

500

6600

7700

8800

9

900

5

300

6450

7600

8750

9

900

# 10.KATIEMin.0

1Dist.0

100

(c.) How far had Katie walked before John caught her?

Min.0

1 2 3 4Dist.0

150

JOHN

2

200

3

300

4

400

5

500

6600

7700

8800

9

900

5

300

6450

7600

8750

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 7212 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 = t10/15 = 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 TimeAaron 50 mph 3 hoursBill 60 mph 2.5 hoursColby 40 mph 4 hoursDillon 55 mph 2 hours and 30 min

d = r t150 mi150 mi80 mi137.5 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 TimeEdgar 100

miles1.25 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 mphHelen 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.