Question : The speed of two railway engines is in the ratio 5 : 4. If they move on parallel tracks in the same direction and if the slower engine is ahead of the faster engine by 8 km when the latter starts, then how far will the faster engine have to travel before it overtakes the slower one?
Option 1: 32
Option 2: 48
Option 3: 40
Option 4: 36
Correct Answer: 40
Solution :
Given: The speed of two railway engines is in the ratio 5 : 4.
Let the speed of the faster engine, $S_1=5$ km/hr
and the speed of the slower engine, $S_2=4$ km/hr
Relative speed = $5-4=1$
Distance between two engines = 8 km
Now,
Required time to overtake by faster engine = $\frac{8}{1}=8$ hours
Distance covered by the faster engine in 8 hours = 8 × 5 = 40 km
Hence, the correct answer is 40.
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