# AVERAGE SPEED WORD PROBLEMS WORKSHEET WITH ANSWERS

Average speed word problems worksheet with answers is much required to the students who want practice problems on average speed.

Before, we look at average speed word problems worksheet with answers, let us come to know the formula for average speed.

Formula for average speed, (Different distances covered in different speeds)

If a person travels from A to B at some speed, say "x" miles per hour. He comes back from B to A at different speed, say "y" miles per hour. Both the ways, he covers the same distance, but at different speeds.

Then, the formula is to find the average speed for the whole journey is given below.

## Average speed word problems worksheet with answers

Let us look at average speed word problems worksheet with answers

1. David drove for 3 hours at a rate of 50 miles per hour, for 2 hours at 60 miles per hour and for 4 hours at a rate of 70 miles per hour. What was his average speed for the whole journey ?

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

3. Jose travels from the place A to place B at a certain speed. When he comes back from place B to place A, his speed is 60 miles per hour.If the average speed for the whole journey is 72 miles per hour, find his speed when he travels from the place A to B.

4. 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.

5. David travels from the place A to place B at a certain speed. When he comes back from place B to place A, he increases his speed 2 times. If the constant-speed for the whole journey is 80 miles per hour, find his speed when he travels from the place A to B.

6. 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.

7. A person takes 5 hours to travel from place A to place B at the rate of 40 miles per hour. He comes back from place B to place A with 25% increased speed. Find the average speed for the whole journey.

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.

9. Speed ( A to B )  =  20 miles/hour,

Speed (B to C )  =  15 miles/hour,

Speed (C to D )  =  30 miles/hour

If the distances from A to B, B to C and C to D are equal and it takes 3 hours to travel from A to B, find the average speed from A to D

10. 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

## Do you need answers for the above questions ?

Here they are.

Now, let us look at step by step solution for the problems given on "Average speed word problems worksheet with answers"

Problem 1 :

David drove for 3 hours at a rate of 50 miles per hour, for 2 hours at 60 miles per hour and for 4 hours at a rate of 70 miles per hour. What was his average speed for the whole journey ?

Solution :

Step 1 :

Formula for average speed  =  Total distance / Total time taken.

And also, for for distance  =  Rate x Time

Step 2 :

Distance covered in the first 3 hours  =  50 x 3  =  150 miles

Distance covered in the next 2 hours  =  60 x 2  =  120 miles

Distance covered in the last 4 hours  =  70 x 5  =  350 miles

Step 3 :

Then, total distance  =  150 + 120 + 350  =  620 miles

Total time  =  3 + 2 + 5  = 10 hours

Step 4 :

So, average speed  =  620 / 10  =    62 miles per hour

Hence, the constant speed for the whole journey is 62 miles per hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

Problem 2 :

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

Solution :

Step 1 :

Here, both the ways, he covers the same distance.

Then, formula for constant speed  =  2xy / (x+y)

Step 2 :

x ----> Rate at which he travels from Newyork to Washington

x  =  45

y ----> Rate at which he travels from Newyork to Washington

y  =  55

Step 3 :

So, average speed  =  2(45)(55) / (45+55)

Average speed  =  4950 / 100

Average speed  =  49.5 miles per hour

Hence, the average speed for the whole journey is 45 miles per hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

Problem 3 :

Jose travels from the place A to place B at a certain speed. When he comes back from place B to place A, his speed is 60 miles per hour.If the average speed for the whole journey is 72 miles per hour, find his speed when he travels from the place A to B.

Solution :

Step 1 :

Let "a" be the speed from place A to B.

Speed from place B to A  =  60 miles/hour

Step 2 :

Here, both the ways, he covers the same distance.

Then, formula for constant-speed  =  2xy / (x+y)

Step 3 :

x ----> Speed from place A to B

x  =  a

y ----> Speed from place B to A

y  =  60

Step 4 :

Given : Average speed  =  72 miles/hour

2(a)(60) / (a+60)  =  72

120a  =  72(a+60)

120a  =  72a + 4320

48a  =  4320

a  =  90

Hence, the average speed from place A to B is 90 miles per hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

Problem 4 :

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.

Solution :

Step 1 :

Walking + Walking  =  10 hours ---------> walking  =  5 hours

Riding + Riding  =  8  hours    (Because 2 hours gained)

Then, Riding  =  4 hours

Walking + Riding --------> ( 5 + 4 )  =  9 hours

Step 2 :

Total time taken  =  9 hours

Total distance covered  =  18 miles

Step 3 :

So, average speed  =  Total distance / Total time

=  18 / 9

=  2 miles per hour

Hence, the required average speed is 2 miles per hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

Problem 5 :

David travels from the place A to place B at a certain speed. When he comes back from place B to place A, he increases his speed 2 times. If the constant-speed for the whole journey is 80 miles per hour, find his speed when he travels from the place A to B.

Solution :

Step 1 :

Let "a" be the speed from place A to B.

Then, speed from place B to A  =  2a

Step 2 :

Here, both the ways, he covers the same distance.

Then, formula for constant speed  =  2xy / (x+y)

Step 3 :

x ----> Speed from place A to B

x  =  a

y ----> Speed from place B to A

y  =  2a

Step 4 :

Given : Average speed  =  80 miles/hour

2(a)(2a) / (a+2a)  =  80

4a² / 3a  =  80

4a / 3  =  80

a  =  60

Hence, the speed from place A to B is 60 miles per hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

Problem 6 :

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.

Solution :

Step 1 :

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

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

Step 2 :

Formula for distance  =  Rate x Time

Distance (A to B) =  60 x 3  =  180 miles

Distance (B to C) =  90 x 2  =  180 miles

Total distance traveled  =  360 miles

Total time taken  =  3 + 2  =  5 hours

Step 3 :

Formula for average speed  =  Total distance / Total time

=  360 / 5

=  72

Hence, the average speed from place A to B is 72 miles/hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

Problem 7 :

A person takes 5 hours to travel from place A to place B at the rate of 40 miles per hour. He comes back from place B to place A with 25% increased speed. Find the average speed for the whole journey.

Solution :

Step 1 :

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

Speed ( from B to A )  =  50 miles/hour  (25% increased)

Step 2 :

Formula for distance  =  Rate x Time

Distance (A to B)  =  40 x 5  =  200 miles

Total distance  =  200 + 200  =  400 miles

Time (A to B)  =  5 hours

Time (B to A)  =  Distance / Speed  =  200 / 50  =  4 hours

Total time  =  5 + 4  =  9 hours

Step 3 :

Formula for average speed  =  Total distance / Total time

=  400 / 9

=  44.44

Hence, the average speed for the whole journey is 44.44 miles/hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

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.

Solution :

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 for Time  =  Distance / Speed

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 (from A to D)  =  5 + 5 + 6  =  16 hours

Total distance (from A to D)  =  200 + 300 + 540  =  1040 miles

Step 3 :

Formula for average speed  =  Total distance / Total time

=  1040 / 16

=  65

Hence, the average speed from A to D is 65 miles per hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

Problem 9 :

Speed ( A to B )  =  20 miles/hour,

Speed (B to C )  =  15 miles/hour,

Speed (C to D )  =  30 miles/hour

If the distances from A to B, B to C and C to D are equal and it takes 3 hours to travel from A to B, find the average speed from A to D

Solution :

Step 1 :

Formula for distance  =  Rate x Time

Distance from A to B  =  20 x 3  =  60 miles

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

Total distance (A to D)  =  60 + 60 + 60  =  180  miles

Step 2 :

Formula for Time  =  Distance / Speed

Time (A to B)  =  60 / 20  =  3 hours

Time (B to C)  =  60 / 15  =  4 hours

Time (C to D)  =  60 / 30  =  2 hours

Total time (from A to D)  =  3 + 4 + 2  =  9 hours

Step 3 :

Formula for average speed  =  Total distance / Total time

=  180 / 9

=  20

Hence, the average speed from A to D is 20 miles per hour.

Let us look at the next problem on "Average speed word problems worksheet with answers"

Problem 10 :

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

Solution :

Step 1 :

Formula for distance  =  Rate x Time

Distance from A to B  =  70 x 3  =  210 miles

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

Total distance (A to D)  =  210 + 210 + 210  =  630  miles

Total time (A to D)  =  3 + 5 + 6  =  14

Step 2 :

Formula for constant speed  =  Total distance / Total time

=  630 / 14

=  45

Hence, the constant speed from A to D is 45 miles per hour.

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