Points A and B are 70 km. apart 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 they travel towards each other, they meet in one hour. Find the speed of the two cars.

Given:

Points A and B are 70 km. apart 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 they travel towards each other, they meet in one hour.

To do:

We have to find the speed of the two cars.

Solution:

We know that,

Distance$=$ Speed $\times$ Time.

Distance between the two points A and B $= 70\ km$.

Let the speed of the first car starting from A be $x\ km/hr$ and the speed of the second car starting from B be $y\ km/hr$.

Let the cars meet at point P when they are moving in the same direction and at point Q when they are moving in the opposite direction.

When they travel in the same direction, they meet in 7 hours.

Distance travelled by the first car in 7 hours $AP= 7\times x\ km=7x\ km$.

Distance travelled by the second car in 7 hours $BP= 7\times y\ km=7y\ km$.

$AP-BP=70$

$7x-7y=70$

$7(x-y)=7\times10$

$x-y=10$.....(i)

When they travel in the opposite direction, they meet after 1 hour.

Distance travelled by the first car in 1 hour $AQ= 1\times x\ km=x\ km$.

Distance travelled by the second car in 1 hour $BQ= 1\times y\ km=y\ km$.

$AQ+BQ=AB$

$x + y = 70$….(ii)

Adding equations (i) and (ii), we get,

$x-y+x+y=10+70$

$2x = 80$

$x = \frac{80}{2}$

$x=40$

Substituting $x=40$ in equation (i), we get,

$40+y=70$

$y = 70-40$

$y = 30$

Therefore, the speed of the first car is $40\ km/hr$ and the speed of the second car is $30\ km/hr$.

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Updated on: 10-Oct-2022

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