## Speed, Time and Distance

#### Speed, Time and Distance

1. A boy runs 20 km in 2.5 hours. How long will he take to run 32 km at double the previous speed ?
1. 2 hours
2.  2 1 hours 2
3.  4 1 hours 2
4. 5 hours

1. The boy covers 20 km in 2.5 hours.

 ⇒ Speed = 20 = 8 km/hr. 2.5

New speed = 16 km/hr
 ∴ Time = 32 = 2 hours. 16

##### Correct Option: A

The boy covers 20 km in 2.5 hours.

 ⇒ Speed = 20 = 8 km/hr. 2.5

New speed = 16 km/hr
 ∴ Time = 32 = 2 hours. 16

1. A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, the distance between his house and school is :
1. 6 km
2. 5 km
3. 5.5 km
4. 6.5 km

1. Let the required distance be x km.
Then,

 x + x = 5 3 2

 ⇒ 2x + 3x = 5 6

⇒  5x = 6 × 5
 ∴  x = 6 × 5 = km 5

Second Method :
Here, x = 3, y = 2
 Average Speed = 2 × x × y x + y

 = 2 × 3 × 2 3 + 2

 = 12 km/hr 5

 Total distance = 12 × 5 = 12km 5

 ∴  Required distance = 12 = 6 km 2

##### Correct Option: A

Let the required distance be x km.
Then,

 x + x = 5 3 2

 ⇒ 2x + 3x = 5 6

⇒  5x = 6 × 5
 ∴  x = 6 × 5 = km 5

Second Method :
Here, x = 3, y = 2
 Average Speed = 2 × x × y x + y

 = 2 × 3 × 2 3 + 2

 = 12 km/hr 5

 Total distance = 12 × 5 = 12km 5

 ∴  Required distance = 12 = 6 km 2

1. A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the
rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was
1. 25 km
2. 30 km
3. 20 km
4. 15 km

1. Let the distance be x km.
Total time = 5 hours 48 minutes

 = 5 + 48 = 5 + 4 hours 60 5

 = 29 hours 5

 ∴ x + x = 29 25 4 5

 ⇒ 4x + 25x = 29 100 5

⇒  5 × 29x = 29 × 100
 ⇒  x = 29 × 100 = 20 km. 5 × 29

Second Method :
Here, x = 25, y = 4
 Average speed = 2xy x + y

 = 2 × 25 × 4 = 200 25 + 4 29

 Total Distance = 200 × 5 4 29 5

 = 200 × 29 = 40 km 29 5

##### Correct Option: C

Let the distance be x km.
Total time = 5 hours 48 minutes

 = 5 + 48 = 5 + 4 hours 60 5

 = 29 hours 5

 ∴ x + x = 29 25 4 5

 ⇒ 4x + 25x = 29 100 5

⇒  5 × 29x = 29 × 100
 ⇒  x = 29 × 100 = 20 km. 5 × 29

Second Method :
Here, x = 25, y = 4
 Average speed = 2xy x + y

 = 2 × 25 × 4 = 200 25 + 4 29

 Total Distance = 200 × 5 4 29 5

 = 200 × 29 = 40 km 29 5

1. A car travelling at a speed of 40 km/hour can complete a journey in 9 hours. How long will it take to travel the same distance at 60 km/hour ?
1. 6 hours
2. 3 hours
3. 4 hours
4.  4 1 hours 2

1. Total distance covered
= Speed × Time
= 40 × 9 = 360 km.
The required time at 60 kmph

 = 360 = 6 hours. 60

Second Method :
Using Rule 9,
Here, S1 = 40, t1 = 9
S2 = 60, t2 = ?
S1t1 = S2t2
40 × 9 = 60 × t2
 t2 = 4 × 9 = 6 hours. 6

##### Correct Option: A

Total distance covered
= Speed × Time
= 40 × 9 = 360 km.
The required time at 60 kmph

 = 360 = 6 hours. 60

Second Method :
Using Rule 9,
Here, S1 = 40, t1 = 9
S2 = 60, t2 = ?
S1t1 = S2t2
40 × 9 = 60 × t2
 t2 = 4 × 9 = 6 hours. 6

1. A car goes 10 metres in a second. Find its speed in km/hour.
1. 40
2. 32
3. 48
4. 36

1. Speed of car = 10 m/sec.
Required speed in kmph

 = 10 × 18 = 36 km/hr 5

##### Correct Option: D

Speed of car = 10 m/sec.
Required speed in kmph

 = 10 × 18 = 36 km/hr 5