Question 31

An express train makes run 240 km t a certain speed. Another train whose speed is 12 km/hr less takes an hour longer to make the same trip. Find the speed of the express train.

Solution:

Let “x” be speed of express train

Another train whose speed is 12 km/hr less than the speed of express train

So “x – 12” be the speed of another train

Distance to be covered = 240 km

Let T1 be the time taken by the train to cover the distance 240 km at the speed of x km/hr

Let T2 be the time taken by the train to cover the distance 240 km at the speed of (x + 12) km/hr

Time = Distance /speed

T1 = 240/x

T2 = 240/(x - 12)

T2 - T 1 = 1 hour

[240/(x- 12)] - [240/x] = 1

240[(1/(x -12) - 1/x] = 1

240[(x - x + 12)/x(x - 12)] = 1

240[12/(x² - 12 x)] = 1

2880 = (x² - 12 x)

x² - 12 x - 2880 = 0

x² + 60 x - 48 x - 2880 = 0

x(x + 60)- 48 (x + 60) = 0

(x - 48) (x + 60) = 0

x - 48 = 0           x + 60 = 0

x = 48              x = -60

Here x represents the speed of the train. So we should not take the negative value - 60 for x.

Speed of express train = 48 km/hr

Speed other train = (x - 12) = (48 - 12) = 36 km/hr

Verification:

Time = Distance/speed

Time taken by the express train to cover 240 km = 240/48

= 5 hours

Time taken by the another train to cover 240 km = 240/36

= 6 hours

difference of time taken = 6 - 5 = 1 hour