Question : A car moving in the morning fog passes a man walking at 4 km/hr in the same direction. The man can see the car for 3 minutes and visibility is up to a distance of 130 m. The speed of the car is:
Option 1: $7\frac{3}{5}$ km/hr
Option 2: $6\frac{3}{5}$km/hr
Option 3: $7$ km/hr
Option 4: $5$ km/hr
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Correct Answer: $6\frac{3}{5}$km/hr
Solution :
Speed of man = 4 km/hr
Let $x$ be the speed of the car.
As they are moving in the same direction, relative speed = $(x-4)$ km/hr
⇒ Distance, d = $\frac{130}{1000}$km = 0.13 km
⇒ Time, t = $\frac{3}{60}$hr = 0.05 hr
So, Speed = $\frac{\text{Distance}}{\text{Time}}$
⇒ $(x-4)$ = $\frac{0.13}{0.05}$
$\therefore x = 4+\frac{13}{5}=\frac{33}{5}=6\frac{3}{5}$ km/hr
Hence, the correct answer is $6\frac{3}{5}$ km/hr.
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