# Solved Example

Distance covered in 2min = 20 Ã— 2 Ã— 60 = 2400 m

If a man runs at 3 m/s. How many km does he run in 1 hr 40 minutes?

Speed of the man = 3 Ã— 18/5 km/h = 54/5 km/h

Distance covered in 5/3 hrs = 54/5 Ã— 5/3 = 18k m

4 Ã— 11/4 = 11 km

New speed = 16.5 km/h

Therefore Time = D/S = 11/16.5 = 40 min

A train covers a distance in 50 min, if it runs at a speed of 48 km/h on an average. The speed at which the train must run to reduce the time of journey to 40 min will be.

Time = 50/60 hr = 5/6 hr

Speed = 48mph

Distance = S Ã— T = 48 Ã— 5 /6 = 40 km

Time = 40/60 hr = 2/3 hr

New speed = 40 Ã— 3/2 km/h = 60 km/h

Total time = 1 hr 24 min

A to T:

Speed = 4 km/h Distance = 2/3S

T to S:

Speed = 5 km/h Distance = 1 - 2/3 S = 1/3 S

= > 21/15 hr = 2/3 S/4 + 1/3S/5

= > 84 = 14/3S Ã— 3

S = 84 Ã— 3/14 Ã— 3 = 6 km

Walking at Â¾ of his usual speed, a man is late by 2Â½ hr. The usual time is?

Usual speed = S Usual time = T Distance = D

New Speed is 3/4 S

New time is 4/3 T

4/3 T â€“ T = 5/2

T = 15/2 = 7 Â½

x/y â€“ x/y + 3 = 40/60 hr

2y (y + 3) = 9x [Eqn 1]

x/y - 2 â€“ x/y = 40/60 hr y(y - 2) = 3x [Eqn 2]

Divide 1 & 2 and solving we get

x = 40

Excluding stoppages, the speed of the bus is 54 km/h and including stoppages, it is 45 km/h. For how many min does the bus stop per hr?

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km is [9/54 Ã— 60] min = 10 min

Distance between them is 8.5 km

Time = 8.5/0.5 = 17 hrs

Two trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

In same time, they cover 110 km & 90 km respectively

So ratio of their speed = 110:90 = 11:9

Then distance covered by the second train is x + 120 km

x/50 = x + 120 / 60

x = 600

So the distance between A & B is x + x + 120 = 1320 km

A thief steals a car at 2.30 pm and drives it at 60 km/h. The theft is discovered at 3pm and the owner sets off in another car at 75 km/h when he will overtake the thief.

Let the thief is overtaken x hrs after 2.30pm

Distance covered by the thief in x hrs = distance covered by the owner in x - 1/2 hr

60x = 75 (x - Â½)

x = 5/2 hr

Thief is overtaken at 2.30 pm + 2 Â½ hr = 5 pm

Let A takes 4x hrs, B takes 3x hrs

Then 4x - 3x = 30/60 hr

x = Â½ hr

Time taken by A to reach the destination is 4x = 4 x Â½ = 2 hr

A motorist covers a distance of 39 km in 45 min by moving at a speed of x km/h for the first 15 min. Then moving at double the speed for the next 20 min and then again moving at his original speed for the rest of the journey. Then x = ?

Total distance = 39 km Total time = 45 min

D = S x T

X Ã— 15/60 + 2x Ã— 20/60 + x Ã— 10/60 = 39 km

x = 36 km/h

= 2xy / x + y = 10.88 km/h

A car covers 4 successive 3 km stretches at speed of 10 km/h, 20 km/h, 30 km/h & 60 km/h respectively. Its average speed is.

Average speed = total distance / total time

Total distance = 4 Ã— 3 = 12 km

Total time = 3/10 + 3/20 + 3/30 + 3/60 = 36/60 hr

Speed = 12/36 Ã— 60 = 20 km/h

A takes 10 min more

3x - 2x = 10 min

A's time = 30 min Thus, A covers the distance in 30 min, if its speed is x

He will cover the same distance in 15 min, if its speed doubles (i.e 2x)

A is twice as fast as B and B is thrice as fast as C is. The journey covered by B in?

Speedâ€™s ratio a : b = 2 : 1 b : c = 3 : 1

Time's ratio b : c = 1 : 3 b : c = 18 : 54

(if c covers in 54 min i.e. twice to 18 min)

They meet after y hr after 7am

M covers x in 4hr

N covers x in 3 Â½ i.e. 7/2 hr

Speed of M = x/4

Speed of N = 2x/7

Distance covered by M in y + 2 hr + Distance covered by N in y hr is x

x/4 (y + 2) + 2x/7(y) = x

y = 14/15 hr or 56 min

A man takes 5 hr 45 min in walking to certain place and riding back. He would have gained 2 hrs by riding both ways. The time he would take to walk both ways is?

Let x be the speed of walked

Let y be the speed of ride

Let D be the distance

Then D/x + D/y = 23/4 hr - - - - - - - 1

D/y + D/y = 23/4 â€“ 2 hr

D/y = 15/8 - - - - - - - - 2

Substitute 2 in 1

D/x + 15/8 = 23/4 - â†’ D/x = 23/4 - 15/8 = 46 - 15/8 = 31/8

Time taken for walk one way is 31/8 hr

Time taken to walk to and fro is 2 Ã— 31/8 = 31/4 hr â†’ = 7 hr 45 min