Question

The distance between two places A and B is 300 metres.rohan starts running from A to B while deepak starts running from B to A.they meet after 4 minutes.if rohan doubled his speed and deepak reduced his by 50%,they would have met one minute earlier.find their speeds

Answer 1

Suppose the speed of Rohan and Deepak are x and y m/s. respectively.
When both Rohan and Deepak met after 4 minutes i.e. 60×4 = 240 seconds
Then distance travelled by Rohan = 240x
And distance travelled by Deepak = 240y
And distance between A and B =  300 m
So we have;
240x+240y = 300⇒4x+4y = 5 ...(i)
Now when Rohan doubled his speed i.e. 2x and Deepak reduces his speed by 50% i.e. y2; then they meet 1 minute earlier i.e. 3 minutes i.e. 180 seconds
Distance travelled by Rohan = 180×2x = 360x
And distance travelled by Deepak = 180×y2 = 90y
Then we have;
360x+90y = 300⇒36x+9y = 30 ...(ii)
Now multiplying (i) by 9 and then subtracting (ii) from (i) we get;
36x+36y−36x−9y = 45−30⇒27y = 15⇒y = 1527 = 59
Then form (ii) we have;
36x+9×59 = 30⇒36x+5 = 30⇒36x = 25⇒x = 2536
Therefore the speed of Rohan is 2536  m/s and the speed of Deepak is 59 m/s