Speed, Time and Distance

Speed, Time and Distance

1. A man walked a certain distance. One-third he walked at 5 km per hr. Another one-third he walked at 10 km per hr. and the rest at 15 km per hr. Find his average speed.
1.  8 1 kmph 11
2.  7 1 kmph 11
3.  7 2 kmph 11
4.  8 2 kmph 11

1. 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

1. 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.
1.  13 2 kmph 3
2.  12 1 kmph 3
3.  13 1 kmph 3
4.  12 2 kmph 3

1. 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

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

1. Case I.
Distance = 10 kms
Speed = 4 km/hr.

 ∴  Time taken (t2) = 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 (t2) = 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

1. 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.?
1.  3 3 hours 4
2. 3 hours
3.  2 3 hours 4
4. 3.5 hours

1. 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

1. A car runs at 60 km per hr. A man runs at one-third the speed of the car and reaches office from his house in 15 minutes. How far is his office from his house?
1. 7 km
2. 5.5 km
3. 6 km
4. 5 km

1.  Man’s speed = 1 of the speed of car 3
 = 1 × 60 = 20 km per hr. 3

Time taken to reach office= 15
 minutes = 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= 15
 minutes = 15 = 1 hr. 60 4

∴  Distance between his house and office
= Speed × Time
 = 20 × 1 = 5 km. 4