Question

The distance between two stations is $300km.$ Two motor-cyclists start simultaneously from these stations and move towards each other. The speed of one of them is $7km/h$ more than that of the other. If the distance between them after $2$ hours of their start is $34km$, find the speed of each motor-cyclist. Check your solution.

Answer 1

According to the question after time $2h$

$300=(v+7)2+34+v2$ [dist$=$ velocity$\times$ time]

$300=2v+14+34+2v$

$300=4v+48$

$4v=252$

$v=63$ km/h

Check: Put $v=63$ in the equation then RHS converts to

$(63+7)2+34+63\times 2$

$70\times 2+34+63\times 2$

$140+34+126$

$300$

Which is equal to LHS.