## Speed, Time and Distance

#### Speed, Time and Distance

1. If a train runs at 5/6 of its original speed, then it reaches the station 10 min late. Then find out the usual time taken by train to cover the distance.
1. 40 min
2. 45 min
3. 50 min
4. 55 min

1. Assume the actual speed of train be x and actual time taken be y

And, distance is same in both case

##### Correct Option: C

Let the actual speed of train be x and actual time taken be y

Then new speed of train = 5x/6

Therefore, new time taken = 6y/5 (as distance is same in both case)

Given, 6y/5 - y = 1/6 hr , therefore actual time = 50 min

1. A car is moving with the speed of 47.52km/hr and the radius of the wheel of car is 21 cm. Calculate the approximate number of revolutions made by the wheel in one minute.
1. 250 rpm
2. 200 rpm
3. 600 rpm
4. 300 rpm

1. Circumference of circle = 2πr
Where r = radius of circle

##### Correct Option: C

Speed in cm/minute = (Speed in km/hr x 1000 x100 )/60
= 47.52x(50/3)
=79200 cm/min

And Circumference of circle = 2πr
=2 x ( 22 / 7 ) x 21
=132

No. of revolutions = ( Speed in cm/minute ) / circumference of circle in cm
=79200 / 132
=600 rpm

1. A man walking at 3km/hr crosses a square field diagonally in 2 min. The area of the field is ?
1. 25 acres
2. 30 acres
3. 50 acres
4. 60 acres

1. speed = 3 x ( 5/18 ) m/sec.
= 5 / 6 m/sec.

∴ Distance covered in 2 min. = ( 5 / 6) x 2 x 60 m
= 100 m.

∴ Length of diagonal = 100 m

##### Correct Option: C

speed = 3 x ( 5/18 ) m/sec.
= 5 / 6 m/sec.

∴ Distance covered in 2 min. = ( 5 / 6) x 2 x 60 m
= 100 m.

∴ Length of diagonal = 100 m

Area of the field = 1/2 x diagonal2
=1/2 x 100 x 100 m2
= 5000 m2
= 50 acres.

1. A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is ?
1. 4:1
2. 1.4
3. 2:1
4. 1:2

1. Let x km . be covered in y hrs.
then, 1st speed = (x / y) km/hr.

2nd speed = [(x/2) / 2y)] km/hr.
= (x/4y) km/hr.

##### Correct Option: A

Let x km . be covered in y hrs.
then, 1st speed = (x / y) km/hr.

2nd speed = [(x/2) / 2y)] km/hr.
= (x/4y) km/hr.

∴ Ratio of speed = x/y : x/4y = 1 :1/4 = 4: 1

1. A is twice as fast as B and B is thrice as fact as C is . The journey covered by C in 42 minute, will be covered by A in ?
1. 14 min
2. 28 min
3. 63 min
4. 7 min

1. Let C' s speed = x km/hr.
Then, B's speed = 3x km/hr.
and A's speed = 6x km/hr.

∴ Ratio of speed of A, B, C
= 6x : 3x : x = 6 : 3 : 1

Ratio of times taken = 1/6 : 1/3 : 1 or 1 : 2 : 6

##### Correct Option: D

Let C' s speed = x km/hr.
Then, B's speed = 3x km/hr.
and A's speed = 6x km/hr.

∴ Ratio of speed of A, B, C
= 6x : 3x : x = 6 : 3 : 1

Ratio of times taken = 1/6 : 1/3 : 1 or 1 : 2 : 6

∵ 6 : 1 : : 42 : t
⇒ 6t = 42
⇒ t = 7 min.