Question : If a train maintains an average speed of 42 km/hr, it arrives at its destination at the right time. If however, the average speed is 40 km/hr, it arrives 15 minutes late. Find the distance of the journey.
Option 1: 210 km
Option 2: 205 km
Option 3: 209 km
Option 4: 200 km
Correct Answer: 210 km
Solution :
Let the time be $x$ hours when the train moves at a speed of 42 km/hr.
So, time will be $(x+\frac{1}{4})$ hours when the train moves at a speed of 40 km/hr.
(15 minutes = $\frac{1}{4}$ hour)
Distance = Speed × Time
$⇒42×x = 40 × (x+\frac{1}{4})$
$⇒2x=10$
$\therefore x=5$
Total distance = 42 × 5 = 210 km
Hence, the correct answer is 210 km.
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