Albert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Let's Assume the distance travelled Albert = x km.
Formula Used: Time = Distance/Speed
so (x/10 - x/15) = 2 hrs
=> (3x - 2x)/30 = 2 hrs.
=> (3x - 2x) = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 hrs = 6 hrs.
Formula Used: Speed = Distance/Time
So, Albert started 6 hours before 2 P.M. i.e @ 8 A.M.
Required speed = 60/5 kmph. = 12 kmph.
Workspace
NA
SHSTTON
89
Solv. Corr.
80
Solv. In. Corr.
169
Attempted
1 M:38 S
Avg. Time
5 / 88
Choose the correct option.
Raghav had to walk a certain distance. He walked half the distance at a speed of 4 km/hour and the remaining half at a speed of 5 km/hour. If the total time taken was 9 hour, the distance was
Let half of the distance travelled be d.
Time taken at the speed of 4 km/hr = (d/4)
Time taken at the speed of 5 km/hr = (d/5)
Therefore, total time = (d/4) + (d/5) = 9 hrs.
? (5d + 4d)/20 = 9
? 9d = 180
? d = 20.
Therefore total distance = d x 2 = 40 kms
Workspace
NA
SHSTTON
63
Solv. Corr.
78
Solv. In. Corr.
141
Attempted
2 M:22 S
Avg. Time
6 / 88
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Virat travelled 75 kms in 7 hours. He went some distance at the rate of 12 km/hr and the rest at 10 km/hr. How far did he travel at the rate of 12 km/hr?
Let the distance travelled at the rate of 12 kmph be x km
Time taken to travel this distance = x/12 .......(1)
Then the distance travelled at the rate of 10 km/hr will be (75 - x)
Time taken to travel this distance = (75 - x)/10 .......(2)
Total time taken to cover the total distance = 7 hrs
=>(x/12) + (75 - x)/10 = 7 [sum of (1) and (2)]
=> (10x + 900 - 12x) = 840
=> -2x = -60
=> x = 30.
Therefore, the distance travelled at the rate of 12 km/hr = 30km.
Workspace
NA
SHSTTON
43
Solv. Corr.
73
Solv. In. Corr.
116
Attempted
1 M:30 S
Avg. Time
7 / 88
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A boy rides his bicycle 10 kms at an average speed of 12 kmph and again travels 12 kms at an average speed of 10 kmph. His average speed for the entire trip is approximately:
Average speed is represented by total distance divided by the time taken.
Total distance = 10 kms + 12 kms = 22 kms
Total Time = (10/12) + (12/10)
? (10/12) + (12/10) = (100 + 144)/120 = 244/120 hrs
Average speed = 22/(244/120) = 10.8 kmph.
Average speed for the entire trip is 10.8 kmph.
Workspace
NA
SHSTTON
69
Solv. Corr.
46
Solv. In. Corr.
115
Attempted
0 M:0 S
Avg. Time
8 / 88
Choose the correct option.
An athlete runs half of the distance at the speed of 10 km/hr and remaining 15 km at the speed of 20 km/hr, how much time will be taken to cover the total distance?
We know that time = distance/speed
Time taken by the athlete for the first half = 15/10
And time taken by the athlete for the second half = 15/20
Total time = 15/10 + 15/20 = (45/20) x 60 = 135 mins
Time taken to cover the total distance is 135 mins.
Workspace
NA
SHSTTON
70
Solv. Corr.
76
Solv. In. Corr.
146
Attempted
1 M:21 S
Avg. Time
9 / 88
Choose the correct option.
A person travelled by train for 1 hour at a speed of 50 kmph. He then travelled by a taxi for 30 minutes at a speed of 32 kmph to complete his journey. What is the average speed at which he travelled during the journey?
Time = Distance/Speed
Time taken for each 6 km can be given by
6/25, 6/50, 6/75 and 6/150
Total time = (6/25) + (6/50) + (6/75) + (6/150) = (36 + 18 + 12 + 6)/150 = 72/150
Average speed = Distance/time = (24/72) x 150 = 50 kmph
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