Question

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

Answer 1

The distance between two stations = 300 km

Let the speed of first motorcyclists = x km/h

and speed of second motorcyclists = (x + 7) km/h

Distance covered by the first = 2x km

and distance covered by the second = 2 (x + 7) km = 2x + 14 km

$\therefore$ Distance uncovered by them = 300 - (2x + 2x + 14) kms.

According to the condition,

300 - (4x + 14) = 34

$\Rightarrow$ 300 - 4x - 14 = 34

$\Rightarrow$ 300 - 14 - 34 = 4x

$\Rightarrow$ 4x = 300 - 48

$\Rightarrow$ 4x = 252 $\Rightarrow x=\frac{252}{4}=63$

$\therefore$ Speed of the first motorcyclists = 63 km/h

and speed of second = 63 + 7 = 70 km/h

Check. Distance covered by both of them

= 2 $\times$ 63 + 2 $\times$ 70 = 126 + 140 = 266

Total distance = 300 km.

$\therefore$ Distance between them = 300 - 266 = 34 km.

which is given.