Question

22. A and B are 2 points 150 km apart on a highway. 2 cars start with different speeds from A and B at the same time. If they move in the same direction, they meet in 15h but of they move in the opposite directions, they meet in 15h but if they move in the opposite directions, they meet in 1h. Find their speed.

Answer 1

Answer :

Speed of car X = 80 km/h

Speed of car Y = 70 km/h

Given :

Distance between points A & B = 150 km

Time taken to meet (travelling same direction) = 15 hours

Time taken to meet (travelling opposite direction) = 1 hour

To Find :

Speed of the two cars (X & Y).

How To Find :

Let X and Y be the two cars starting from point A and B.

Now, let the speed of car C be x km/h and that of Y be y km/h.

▶ Case Ⅰ :

When two cars are moving in the same direction.

Let these cars meet at point G. Then,

Distance travelled by car X = AG

Distance travelled by car Y = BG

It is given that two cars meet in 15 hours.

∴ Distance travelled by car X in 15 hours = 15x km.

∴ AG = 15x

Distance travelled by car Y in 15 hours = 15y km.

∴ BG = 15y

We know, AG - BG = AB

⇝ 15x - 15y = 150

⇝ x - y = 10 $\longrightarrow{(1)}$

▶ Case Ⅱ :

When two cars move in opposite directions.

Let these cars meet at point P. Then,

Distance travelled by car X = AP

Distance travelled by car Y = BP

In this case, two cars meet in 1 hour.

∴ Distance travelled by car X in 1 hour = x km.

∴ AP = x

Distance travelled by car Y in 1 hour = y km.

∴ BP = y

We know, AP + BP = AB

⇝ x + y = 150 $\longrightarrow{(2)}$

$\rule{200}3$

Adding (1) and (2), we get,

⇝ 2x = 160

⇝ x = 160/2

⇝ x = 80

Substituting value of x in (1), we get,

⇝ 80 - y = 10

⇝ y = 80 - 10

⇝ y = 70

Hence, speed of car X is 80 km/h and speed of car Y is 70 km/h.