## Speed, Time and Distance

#### Speed, Time and Distance

1. A train cover a distance in 50 minutes, if it runs at a speed of 48 km per hour on an average. The speed at which the train must run to reduce the time of journey to 40 minutes ?
1. 50 km/hr.
2. 55 km/hr.
3. 60 km/hr.
4. 70 km/hr.

1. Total Distance = 48 x (50/60) km.
= 40 km

Required speed = [40 / (40/60)] km.

##### Correct Option: C

Total Distance = 48 x (50/60) km.
= 40 km

Required speed = [40 / (40/60)] km.
= (40 x 60 )/ 40 km/hr.
= 60 km/hr.

1. Excluding stoppages, the speed of a bus is 54 km/hr. and including stoppages it is 45 km/hr. for how many minutes does the bus stop per hour ?
1. 9
2. 10
3. 12
4. 20

1. Due to stoppages, it covers 9 km. less per hour.
Required ans is, time taken to cover 9 km.

##### Correct Option: B

Due to stoppages, it covers 9 km. less per hour

Required time = Time taken to cover 9 km.
= 9 / ( 54 /60) min
= 10 min

1. Two men start together to walk to a certain destination, one at 3.75 km an hour and another at 3 km an hour. The former arrives half an hour before the latter, the distance is ?
1. 9.5 km.
2. 8 km.
3. 7.5 km.
4. 6 km.

1. Let the distance be y km.
From question
y/3 - y/3.75 = 1/2

##### Correct Option: C

Let the distance be y km.
From question
y/3 - y/3.75 = 1/2
⇒ (3.75y - 3y) / (3 x 3.75) = 1/2
⇒ 1.5y= 3 x 3.75
∴ y = ( 3 x 3.75 ) / 1.5
= 7.5 km.

1. A car covers four successive three 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. 10 km/hr.
2. 20 km/hr .
3. 30 km/hr.
4. 25 km/hr .

1. Total time taken = (3/10 + 3/20 + 3/30 + 3/60) hrs.
= 3/5 hrs.

##### Correct Option: B

Total time taken = (3/10 + 3/20 + 3/30 + 3/60) hrs.
= 3/5 hrs.

∴ Average speed = {12 / (3 / 5)} km/hr.
= (12 x 5 ) / 3 km/hr.
= 20 km/hr.

1. A car complete a certain journey in 8 hour. It cover half the distance at 40 km/hr and the rest at 60 km/hr, The length of a journey is ?
1. 350 km.
2. 420 km.
3. 384 km.
4. 400 km.

1. Let the length of total journey be y km.

From question
( y/2 x 1/40 ) + ( y/2 x 1/60) = 8

##### Correct Option: C

Let the length of total journey be y km.

From question
( y/2 x 1/40 ) + ( y/2 x 1/60) = 8
⇒ y/80 + y/120 = 8
⇒ 3y + 2y = 1920
∴ y = 384 km.