AVERAGE SPEED WORD PROBLEMS WORKSHEET WITH ANSWERS
Problem 1 :
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 ?
Problem 2 :
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 3 :
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 4 :
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.
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
Solutions
Problem 1 :
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, the formula to find average speed is
= 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, the average speed is
= (2 ⋅ 45 ⋅ 55) / (45 + 55)
= 4950 / 100
= 49.5
So, the average speed for the whole journey is 45 miles per hour.
Problem 2 :
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 :
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
2 ⋅ Walking = 10 hours
Walking = 5 hours
Given : He could have gained 2 hours by riding both the ways.
That is,
Riding + Riding = 8 hours
2 ⋅ 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 :
So, the average speed is
= Total distance / Total time
= 18 / 9
= 2
So, the required average speed is 2 miles per hour.
Problem 3 :
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 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 :
Formula to find average speed is
= Total distance / Total time
= 360 / 5
= 72
So, the average speed from place A to B is 72 miles/hour.
Problem 4 :
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 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
So, the average speed from A to D is 65 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
Solution :
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 :
Formula to find average speed is
= Total distance / Total time
= 630 / 14
= 45
So, the average speed from A to D is 45 miles per hour.
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