Question
Download Solution PDFA train can travel 75% faster than a car. Both start from point A at the same time and reach point B, 70 kms away from A, at the same time. On the way, however, the train lost about 18 minutes while stopping at the stations. The speed of the car is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A train can travel 75% faster than a car. Both start from point A at the same time and reach point B, 70 km away from A, at the same time. On the way, the train lost about 18 minutes while stopping at the stations.
Formula used:
Let the speed of the car be x km/h.
Then, speed of the train = x + 0.75x = 1.75x km/h
Time taken by car = Distance / Speed = 70 / x hours
Time taken by train = Distance / Speed = 70 / 1.75x hours
Since the train lost 18 minutes (or 18/60 hours), the effective time taken by the train = (70 / 1.75x) + 18/60 hours
Since both reach at the same time, we have:
70 / x = (70 / 1.75x) + 18/60
Calculations:
70 / x = 40 / x + 18 / 60
⇒ 70 / x - 40 / x = 18 / 60
⇒ 30 / x = 18 / 60
⇒ 30 / x = 3 / 10
⇒ x = (30 × 10) / 3
⇒ x = 100
∴ The speed of the car is 100 km/h. The correct answer is option 2.
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