Question

Two towns P and Q are 200 km apart. Bus X starts from Town P and Bus Y starts from Town Q at the same time. If the two buses travel towards each other, they meet after 2 hours. If they travel in the same direction, they cross each other after 8 hours. Find the speed of Bus X.

(Assume that the speeds of the two buses are uniform.)
please answer

Answer 1

P ____________________ Q

We know that PQ = 200 km

Let speed of X bus be x km/hr

Let speed of Y bus be y km/hr

Let's say they meet at R

So

Distance covered in 2 hrs by bus X = speed × time= 2x

i.e., PR = 2x

Distance covered by bus Y in 2 hrs = speed × time = 2y

i.e, QR = 2y

Now

PR + QR = PQ

2x + 2y = 200

2 ( x + y ) = 200

x + y = 100 ........ ( 1 )

In case 2 they meet at a point say S after 8 hours as they travel in same direction

So

Distance covered by X bus in 8 hrs = Speed × time = 8x

i.e., PS = 8x

Similarly

Distance covered by Y bus in 8 hrs= Speed× time = 8y

i.e., QS = 8y

Again

PS - QS = PQ

8x - 8y = 200

8 ( x - y ) = 200

x - y = 25. .......... ( 2 )

Adding ( 1 ) and ( 2 ) , we get

x + y + x - y = 125

2x = 125

x = 62.5 km/ hr

Therefore speed of bus X is 62.5 km/hr