## Speed, Time and Distance

#### Speed, Time and Distance

1. A train travelled at a speed of 35 km/hr for the first 10 minutes and at a speed of 20 km/hr for the next 5 minutes. The average speed of the train for the total 15 minutes is
1. 30 km/hr
2. 23 km/hr
3. 31 km/hr
4. 29 km/hr

1.  Distance covered = 35 × 10 + 20 × 5 km 60 60

 = 35 + 10 km 6 6

 = 45 km 6

Total time = 15 minutes
 = 1 hour 4

 ∴  Required average speed = Distance covered Time taken

 = 45 × 4 6

= 30 kmph

##### Correct Option: A

 Distance covered = 35 × 10 + 20 × 5 km 60 60

 = 35 + 10 km 6 6

 = 45 km 6

Total time = 15 minutes
 = 1 hour 4

 ∴  Required average speed = Distance covered Time taken

 = 45 × 4 6

= 30 kmph

1. A bus covers four successive 3 km stretches at speed of 10 km/hr, 20 km/hr, 30 km/hr and 60 km/hr respectively. Its average speed over this distance is
1. 30 km/hr
2. 25 km/hr
3. 20 km/hr
4. 10 km/hr

1.  Average speed = Total distance Time taken

 = 12 3 + 3 + 3 + 3 10 20 30 60

 = 12 3 6 + 3 + 2 + 1 60

 = 12 × 60 = 20 kmph 3 × 12

##### Correct Option: C

 Average speed = Total distance Time taken

 = 12 3 + 3 + 3 + 3 10 20 30 60

 = 12 3 6 + 3 + 2 + 1 60

 = 12 × 60 = 20 kmph 3 × 12

1. With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 35 km/hr, it is late by 15 minutes. The total journey is
1. 30 km
2. 40 km
3. 70 km
4. 80 km

1. Let the length of journey be x km, then

 x − x = 15 = 1 35 40 60 4

 ⇒ 8x − 7x = 1 280 4

 ⇒  x = 280 = 70 km 4

##### Correct Option: C

Let the length of journey be x km, then

 x − x = 15 = 1 35 40 60 4

 ⇒ 8x − 7x = 1 280 4

 ⇒  x = 280 = 70 km 4

1. P travels for 6 hours at the rate of 5 km/ hour and for 3 hours at the rate of 6 km/ hour. The average speed of the journey in km/ hour is
1.  3 1 5
2.  5 1 3
3.  1 2 9
4.  2 2 5

1. Total distance
= 5 × 6 + 3 × 6
= 30 + 18 = 48 km
Total time = 9 hours

 ∴ Average speed = 48 = 16 = 5 1 kmph 9 3 3

##### Correct Option: B

Total distance
= 5 × 6 + 3 × 6
= 30 + 18 = 48 km
Total time = 9 hours

 ∴ Average speed = 48 = 16 = 5 1 kmph 9 3 3

1. A man covers the journey from a station A to station B at a uniform speed of 36 km/hr and
returns to A with a uniform speed of 45 km/hr. His average speed for the whole journey is :
1. 40 km/hr
2. 40.5 km/hr
3. 41 km/hr
4. 42 km/hr

1. Here same distances are covered at different speeds.

 ∴  Average speed = 2xy kmph x + y

 = 2 × 36 × 45 kmph (36 + 45)

 = 2 × 36 × 45 = 40 kmph 81

##### Correct Option: A

Here same distances are covered at different speeds.

 ∴  Average speed = 2xy kmph x + y

 = 2 × 36 × 45 kmph (36 + 45)

 = 2 × 36 × 45 = 40 kmph 81