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
75
Solv. Corr.
68
Solv. In. Corr.
143
Attempted
1 M:38 S
Avg. Time
3 / 7
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
59
Solv. Corr.
66
Solv. In. Corr.
125
Attempted
1 M:21 S
Avg. Time
4 / 7
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
Workspace
NA
SHSTTON
58
Solv. Corr.
83
Solv. In. Corr.
141
Attempted
1 M:23 S
Avg. Time
6 / 7
Choose the correct option.
Kartik rides a bicycle 8 km/hr and reaches his school 2.5 minutes late. The next day he increases his speed to 10 km/hr and reaches the school 5 minutes early. How far is the school from his house?
Let the total distance be d km. We have speed = 8km/hr and 10km/hr.
We know, time (t) = distance (d)/speed (s).
= > t = d/8 (for the first day)
=> t = d/10 (for the second day)
Difference between the time taken on first day and second day is 2.5 + 5 = 7.5 mins.
Therefore, (d/8) - (d/10) = 7.5/60. (7.5 mins converted to hours)
=> (10d - 8d)/80 = 75/600
=> d = (75 x 80)/1200.
=> d = 5 kms.
Therefore, the distance between his school and house 5 km.
Workspace
NA
SHSTTON
27
Solv. Corr.
76
Solv. In. Corr.
103
Attempted
6 M:7 S
Avg. Time
7 / 7
Choose the correct option.
A cycled from P to Q at 10 kmph and returned at the rate of 9 kmph. B cycled both ways at 12 kmph. In the whole journey B took 10 minutes less than A. Find the distance between P and Q.
Lets assume distance between P and Q = d km.
Time taken by A in both side = d/10 + d/9 = 19d/90 hrs.
Time taken by B in both side = 2d/12 = d/6 hrs.
B tool 10 min. or 1/6 hrs. less than A.
So, 19d/90 - d/6 = 1/6
=> (19d-15d)/90 = 1/6
=> 4d/90 = 1/6
=> d = 15/4 km = 3.75 km.
Workspace
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