Question : With an average speed of 45 km/hr, a train reaches its destination on time. If it goes with an average speed of 30 km/hr, it is late by 15 minutes. The total journey is:
Option 1: 20.5 km
Option 2: 40.5 km
Option 3: 22.5 km
Option 4: 30.5 km
Correct Answer: 22.5 km
Solution :
Let the distance be $d$.
According to the question, the train is late by 15 minutes or $\frac{15}{60}$ hours($\frac{1}{4}$ hours) if the average speed is 30 km/hr instead of 45 km/hr.
Time = $\frac{\text{Distance}}{\text{Speed}}$
⇒ $\frac{d}{45}-\frac{d}{30}=\frac{1}{4}$
⇒ $\frac{3d-2d}{90}=\frac14$
⇒ $d = \frac{90}{4}=22.5$ km
Hence, the correct answer is 22.5 km.
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