Question

Point A and B are 70 km. a part on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if the travel towards each other, the meet in one hour. Find the speed of the two cars.

Answer 1

We have to find the speed of car

Let and be two cars starting from pointsand respectively. Let the speed of car be x km/hr and that of carbe y km/hr.

Case I: When two cars move in the same directions:

Suppose two cars meet at point, Then,

Distance travelled by car

Distance travelled by car

It is given that two cars meet in 7 hours.

Therefore, Distance travelled by car X in hours = km

Distance traveled by car y in 7 hours = km

Clearly

Dividing both sides by common factor 7 we get,

Case II : When two cars move in opposite direction

Suppose two cars meet at point. Then,

Distance travelled by car,

Distance travelled by car.

In this case, two cars meet in 1 hour

Therefore Distance travelled by car X in1 hour km

Distance travelled by car Y in 1 hour km

From the above clearly,

...(ii)

By solving equation (i) and (ii), we get

Substituting in equation (ii) we get

Hence, the speed of car starting from point A is

The speed of car starting from point B is.