### Question 14

SSC-CGL 2020 Mar 4 Shift 3

The distance between two places is 144 km. If two cars are running in the same direction then the faster car takes over the slower car in 12 hours whereas if the cars travel in opposite directions then they cross each other in 9/8 hours. Find the speed of the faster car?

### Solution in Detail

Speed of faster car = $\displaystyle v_F$

Speed of slower car = $\displaystyle v_S$

Case I: Cars travel in same direction

Relative speed is $\displaystyle v_F - v_S$

the relative distance of 144 km was covered in 12 hours, so by speed distance formula,

[1] $\displaystyle v_F - v_S = \frac{144}{12} = 12$

EXPLANATION: Relative speed means the slower car is taken at rest, whereas the other one moves at the relative speed. It may be difficult to visualize, but the distance of 144 km is covered by the faster car travelling at the relative speed.Case II: Cars in opposite direction

Relative speed is $\displaystyle v_F + v_S$

the relative distance of 144 km was covered in 9/8 hours, so

[2] $\displaystyle \therefore \cancel{v_F + v_S = \frac{144}{9/8} = 96}$

Corrected as commented by Preet

[2] $\displaystyle \therefore v_F + v_S = \frac{144}{9/8} = 128$

Adding [1] and [2], $\displaystyle 2v_F = 140$

$\displaystyle v_F = 70 \text{ kph } \underline{Ans}$

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