Question

A train covered. certain distance at a uniform speed if the train would have been 6km/hr faster it would have taken 8 hrs less then the sheduled time and if the train was slower 6km/hr it would have taken 12 hrs more than the sheduled time find the length of the journey​

Answer 1

Let x km/hr be the speed of train

Let y be the time taken by the train

Distance = speed x time

= x y

To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.

it clearly says that speed is increased by 6 and time is reduced by 4

So , (x + 6) (y - 4) = x y

x y - 4 x + 6 y - 24 = x y

x y - x y - 4 x + 6 y = 24

- 4 x + 6 y = 24

divided by (-2) => 2 x - 3 y = -12 ----- (1)

To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.

it clearly says that speed is reduced by 6 and time is increased by 6

So , (x - 6) (y + 6) = x y

x y + 6 x - 6 y - 36 = x y

x y - x y + 6 x - 6 y = 36

6 x - 6 y = 36

divided by (6) => x - y = 6 ----- (2)

2 x - 3 y = -12

(2) x 2 => 2 x - 2 y = 12

(-) (+) (-)

---------------

- y = -24

y = 24

Now we have to apply the value of y in the first equation to get value of x

Substitute y = 24 in the first equation we get

2 x - 3 (24) = -12

2 x - 72 = -12

2 x = -12 + 72

2 x = 60

x = 60/2

x = 30

Speed of the train = 30 km/hr

Time taken by the train = 24 hours

Distance covered by the train = x y = 30 x 24 = 720 km

Verification:

2 x – 3 y = -12

2(30) - 3(24) = -12

60 - 72 = -12

-12 = -12

Hope this helps you

Answer 2

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Let t be the usual time taken by the train to cover the distance

Let d be the distance, s be the usual speed

Usual time taken => d/s = t => d=ts

d/(s+6) = t-4

ts/(s+6) = t-4

ts = ts+6t-4s-24 

6t - 4s - 24 = 0 --> (1)

d/(s-6) = t+6

ts = ts-6t+6s-36

-6t + 6s - 36=0 --->(2)

Solving (1) nd (2), v get

s = 30 km/h

t = 24 hrs

d = t * s

d = 30 * 24 = 720 km

Ans : 720 km