Speed, Time and Distance
 A man walked a certain distance. Onethird he walked at 5 km per hr. Another onethird he walked at 10 km per hr. and the rest at 15 km per hr. Find his average speed.


8 1 kmph 11 
7 1 kmph 11 
7 2 kmph 11 
8 2 kmph 11


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Here, the man covers equal distance at different speeds. Using the formula, the Average Speed is given by
= 3 1 + 1 + 1 5 10 15 = 3 6 + 3 + 2 30 = 90 = 8 2 km per hour. 11 11 Correct Option: D
Here, the man covers equal distance at different speeds. Using the formula, the Average Speed is given by
= 3 1 + 1 + 1 5 10 15 = 3 6 + 3 + 2 30 = 90 = 8 2 km per hour. 11 11
 P and Q are two cities. A boy travels on cycle from P to Q at a speed of 20 km per hr. and returns at the rate of 10 km per hr. Find his average speed for the whole journey.


13 2 kmph 3 
12 1 kmph 3 
13 1 kmph 3 
12 2 kmph 3


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Let the speed between P and Q be x km.
Then time taken to cover x km. P to Q = x hrs. 20
Time taken to cover x km from Q to P at 10 km per hr. P to Q= x hrs. 10
∴ Total distance covered
= x + x = 2x km.
Time taken to cover 2x km.= x + x = x + 2x = 3x hrs. 20 10 20 20 ∴ Average Speed = 2x = 2x × 20 3x/20 3x = 40 km per hr. 3 = 13 1 km per hr. 3
Second Method : Here, x = 20 km per hr.
y = 10 km per hr
∴ Average Speed [∵ Distance is same]= 2xy = 2 × 20 × 10 x + y 20 + 10 = 400 = 40 = 13 1 km per hr. 30 3 3 Correct Option: C
Let the speed between P and Q be x km.
Then time taken to cover x km. P to Q = x hrs. 20
Time taken to cover x km from Q to P at 10 km per hr. P to Q= x hrs. 10
∴ Total distance covered
= x + x = 2x km.
Time taken to cover 2x km.= x + x = x + 2x = 3x hrs. 20 10 20 20 ∴ Average Speed = 2x = 2x × 20 3x/20 3x = 40 km per hr. 3 = 13 1 km per hr. 3
Second Method : Here, x = 20 km per hr.
y = 10 km per hr
∴ Average Speed [∵ Distance is same]= 2xy = 2 × 20 × 10 x + y 20 + 10 = 400 = 40 = 13 1 km per hr. 30 3 3
 A person covers 10 kms at 4 km per hr. and then further 21 kms at 6 km per hr. Find his average speed for whole journey.


5 1 kmph 3 
5 1 kmph 6 
5 1 kmph 2 
4 1 kmph 2


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Case I.
Distance = 10 kms
Speed = 4 km/hr.∴ Time taken (t_{2}) = 21 = 7 hrs. 6 2 Total time taken = 5 + 7 2 2 = 5 + 7 = 6 hrs. 2
Total distance covered
= 10 + 21 = 31 kms∴ Average Speed = Total distance Total time = 31 km per hr. 6 = 5 1 km per hr. 6 Correct Option: B
Case I.
Distance = 10 kms
Speed = 4 km/hr.∴ Time taken (t_{2}) = 21 = 7 hrs. 6 2 Total time taken = 5 + 7 2 2 = 5 + 7 = 6 hrs. 2
Total distance covered
= 10 + 21 = 31 kms∴ Average Speed = Total distance Total time = 31 km per hr. 6 = 5 1 km per hr. 6
 Walking at a speed of 6 km per hour, a man takes 5 hours to complete his journey. How much time will he need to complete the same journey at the rate of 8 km per hr.?


3 3 hours 4  3 hours

2 3 hours 4  3.5 hours


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Speed = 6 km/hr
Time taken = 5 hours
∴ Distance covered
= 6 × 5 = 30 kms
∴ Time required to cover 30 kms
at the speed of 8 km/hr.= Distance = 30 = 15 hours Speed 8 4 = 3 3 hours 4 Correct Option: A
Speed = 6 km/hr
Time taken = 5 hours
∴ Distance covered
= 6 × 5 = 30 kms
∴ Time required to cover 30 kms
at the speed of 8 km/hr.= Distance = 30 = 15 hours Speed 8 4 = 3 3 hours 4
 A car runs at 60 km per hr. A man runs at onethird the speed of the car and reaches office from his house in 15 minutes. How far is his office from his house?

 7 km
 5.5 km
 6 km
 5 km

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Man’s speed = 1 of the speed of car 3 = 1 × 60 = 20 km per hr. 3
Time taken to reach office= 15minutes = 15 = 1 hr. 60 4
∴ Distance between his house and office
= Speed × Time= 20 × 1 = 5 km. 4 Correct Option: D
Man’s speed = 1 of the speed of car 3 = 1 × 60 = 20 km per hr. 3
Time taken to reach office= 15minutes = 15 = 1 hr. 60 4
∴ Distance between his house and office
= Speed × Time= 20 × 1 = 5 km. 4