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Point $A$ and $B$ are $70 km$ apart on a highway. A car starts from $A$ and another car starts from $B$ at the same time. If they travel in the same direction, they meet in $7$ hours, but if they travel towards each other they meet in one hour. What are their speeds?

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40 km / hr

and

30 km / hr

36 km / hr

and

40 km / hr

19 km / hr

and

20 km / hr

40 km / hr

and

50 km / hr

answer is A.

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Detailed Solution

Given two cars at point A and point B.
Let car speed from point

A = xkm / hr

.
And car speed from point

B = ykm / hr

.
Distance = speed

\times

time

∴

Distance from

A = x \times 7 = 7 x

.
Distance from

B = y \times 7 = 7 y

.
If they travel in the same direction, they meet in

7

hours.
Point

A

and

B

are

70 km

apart.

\Rightarrow 7 x - 7 y = 70

\Rightarrow x - y = 10

…….(1)
If they travel towards each other they meet in one hour.

x + y = 70

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

2 x = 80

∴ x = 40

Substituting

x = 40

in (1), we get,

40 - y = 10

∴ y = 30

∴ x = 40 km / hr

and

y = 30 km / hr

.
Therefore, option (1) is correct.

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