A train travels between two stations. The train will be on time if
it runs at an average speed of 60 km/hour, but will be late by 5
minutes if it runs at an average speed of 50 km/hour. What is the
distance between the two stations?

Solution:

Let distance between stations(km) = x

let the time taken (in hrs)when average speed is 60km/hr = t

then the time taken by train when average speed is 50 km/hr = t - 5minutes

= (t - 1/60*5 )hrs

= t-1/12

Note :

60 minutes = one hour

1 minute = 1/60 hour

5 minutes = 5/60 hour

**5 minutes = 1/12 hour **

we know that ,

average speed = total distance / total time taken

therefore ,

according to question ,

60 = d / t.............(Given )

or **t = d/60**

50 = d/ t-1/12 ........ (given)

substitute t in the above equation,

50 = d/ d/60 - 1/12

By Cross Multiplication , we get

50 (d/60 - 1/ 12) = d

50*d/60 - 50*1/12 = d

5/6 d - 50 /12 = d

5/6d -d = 50/12

5d - 6d/6 = 50/12

-d/6 = 50 /12

or -d = 50/12 *6

or -d = 50/2

or -d = 25

Ignoring negative sign ,because distance cannot be negative

** d= 25 km**

Hope this helps you!!