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
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 :
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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