AVERAGE SPEED WORD PROBLEMS WORKSHEET WITH ANSWERS

Problem 1 :

A person travels from New York to Washington at the rate of 45 miles per hour and comes backs to the New York at the rate of 55 miles per hour. What is his average speed for the whole journey?

Problem 2 :

An automobile travels 130 miles in 2.5 hours and 150 miles in 3.5 hours. What is its average velocity over the entire distance traveled?

Problem 3 :

A car travels along a straight road to the east for 120 meters in 5 seconds, then go the west for 60 meters in 1 second. Determine average velocity in meters per sec.

Problem 4 :

A bicyclist travels 19 miles in 1 hour and 45 minutes and  9 miles in 45 minutes. Determine average velocity in miles per hour.

Problem 5 :

Time (A to B) = 3 hours

Time (B to C) = 5 hours

Time (C to D) = 6 hours

If the distances from A to B, B to C and C to D are equal and the speed from A to B is 70 miles per hour, find the average speed from A to D.

Problem 6 :

A man takes 10 hours to go to a place and come back by walking both the ways. He could have gained 2 hours by riding both the ways. The distance covered in the whole journey is 18 miles. Find the average speed for the whole journey if he goes by walking and comes back by riding.   

Problem 7 :

Lily takes 3 hours to travel from place A to place B at the rate of 60 miles per hour. She takes 2 hours to travel from place B to C with 50% increased speed. Find the average speed from place A to C.

Problem 8 :

Distance from A to B = 200 miles

Distance from B to C = 300 miles

Distance from C to D = 540 miles

The speed from B to C is 50% more than A to B. The speed from C to D is 50% more than B to C. If the speed from A to B is 40 miles per hour,  find the average speed from A to D.

1. Answer :

Step 1 :

Both the ways, the covers the same distance.

Then, the formula to find average speed is

= 2xy/(x + y)

Step 2 :

x ----> Rate at which he travels from New York to Washington

x = 45

y ----> Rate at which he travels from New York to Washington

y = 55

Step 3 :

Average speed is

= (2 ⋅ 45 ⋅ 55)/(45 + 55)

= 4950/100

= 49.5 miles/hour

2. Answer :

Step 1 :

Total distance covered :

= 130 + 150

= 130 miles

Step 2 :

Total time :

= 2.5 + 3.5

= 6 hours

Step 3 :

Average speed is

= total distance/total time

  = 120 miles/2.5 hours

= 48 miles/hour

3. Answer :

Step 1 :

Total distance covered :

= 120 + 60

= 180 meters

Step 2 :

Total time :

= 5 + 1

= 6 seconds

Step 3 :

Average speed is

= total distance/total time

= 180 meters/6 seconds

= 60 miles/second

4. Answer :

Step 1 :

Total distance covered :

= 19 + 9

= 28 miles

Step 2 :

Total time :

= 2 hours 45 min + 45 min

= 2 hours +  (45/60) hours + (45/60) hours

= 2 hours + 0.75 hours + 0.75 hours

= 3.5 hours

Step 3 :

Average speed is

= total distance/total time

= 28 miles/3.5 hours

= 8 miles/hour

5. Answer :

Step 1 :

Formula to find distance is

= rate  time

Distance from A to B is

= 70  3

= 210 miles

Given : Distance from A to B, B to C and C to D are equal.

Total distance from A to D is

= 210 + 210 + 210

= 630  miles

Total time taken A to D is

= 3 + 5 + 6

= 14 hours

Step 2 :

Average speed is

= total distance/total time

= 630/14

= 45 miles hour

6. Answer :

Step 1 :

Given : A man takes 10 hours to go to a place and come back by walking both the ways.

That is,

walking + walking = 10 hours

⋅ walking = 10 hours

walking = 5 hours

Given : He could have gained 2 hours by riding both the ways.

That is,

riding + riding = 8  hours

⋅ riding = 8 hours

riding = 4 hours

Step 2 :

If he goes by walking and comes back by riding, time taken by him :

walking + riding = 5 + 4

walking + riding = 9 hours

Step 3 :

total time taken = 9 hours

total distance covered = 18 miles

Step 4 :

Average speed is

= total distance/total time

= 18/9

= 2 miles/hour

7. Answer :

Step 1 :

Speed (from A to B) = 60 miles/hour

Speed (from B to C) = 90 miles/hour (50% increased)

Step 2 :

Formula to find distance is

= rate  time

Distance from A to B is

= 60  3

= 180 miles

Distance from B to C :

= 90  2

= 180 miles

Total distance traveled  from A to B is

= 180 + 180

= 360 miles

Total time taken from A to B is

= 3 + 2

= 5 hours

Step 3 :

Average speed is

= total distance/total time

= 360/5

= 72 miles/hour

8. Answer :

Step 1 :

Speed (from A to B) = 40 miles/hour

Speed (from B to C) = 60 miles/hour (50% more)

Speed (from C to D) = 90 miles/hour (50% more)

Step 2 :

Formula to find time is

= distance/time

time (A to B) = 200/40 = 5 hours

time (B to C) = 300/60 = 5 hours

Time (C to D) = 540/90 = 6 hours

Total time taken from A to D is

= 5 + 5 + 6

= 16 hours

Total distance from A to D is

= 200 + 300 + 540

= 1040 miles

Step 3 :

Formula to find average speed is

= total distance/total time

= 1040/16

= 65 miles hour

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