Question

Two people started simultaneously towards each other from Siliguri and Darjeeling, which are 60 km apart. They met 5 hrs later. After their meeting, the first person, who traveled from Siliguri to Darjeeling, decreased his speed by 1.5 km/h and the other person, who traveled from Darjeeling to Siliguri, increased his speed by 1.5km/h. The first person is known to arrive at Darjeeling 2.5 hours earlier than the second person arrived at Siliguri. Find the initial spped of the first person?

Answer 1

Distance = speed x time
Let speed of first person be x km/h and speed of second person by y km/h.
Set up two simultaneous linear equations this way:
After their meeting, remaining distance for first person is 60km - 5*x km = 60-5x
Time taken for him to complete the journey = (60-5x)/(x-1.5)
After their meeting, remaining distance for first person is 60km - 5*y km = 60-5y
Time taken for him to complete the journey = (60-5y)/(y+1.5)
(60-5x)/(x-1.5) + 2.5 = (60-5y)/(y+1.5) --(1)

Total distance = 5*x + 5*y = 60 --(2)

Solve (1) and (2) simultaneously, you should get x=7.5 and y=4.5
When solving it, if you come across a quadratic and hence negative values, reject the answer since speed > 0.

Now that you have x and y, one of these values should answer your question