A train can travel 60% faster than a car.
A train can travel 60% faster than a car. Both start from point A at the same time and reach point B, which is 60 km away, simultaneously. However, the train loses 20 minutes due to stops at stations. What is the speed of the car?
एक ट्रेन, एक कार से 60% अधिक की चाल से चल सकती है। दोनों एक ही समय पर बिंदु A से चलना शुरू करती हैं और 60 km दूर स्थित बिंदु B पर एक साथ पहुँचती हैं। हालाँकि, यात्रा के दौरान ट्रेन 20 मिनट के लिए स्टेशन पर रुकती है। कार की चाल ज्ञात कीजिए।
Detailed Solution & Logic
67.5 km/h
Step 1: Let the speed of the car be $x$ km/h.
Then the speed of the train = $1.6x$ km/h.
Step 2: Time taken to travel 60 km without stops:
-
Car: $60 / x$ hours
-
Train: $60 / 1.6x = 37.5 / x$ hours
Step 3: Train loses 20 minutes = 1/3 hour due to stops.
Time for train with stops = $37.5 / x + 1/3$ hours
Since both reach simultaneously:
$60 / x = 37.5 / x + 1/3$
Step 4: Solve for $x$:
$60 / x - 37.5 / x = 1/3$
$22.5 / x = 1/3$
$x = 22.5 \cdot 3 = 67.5$
So, the speed of the car is 67.5 km/h.
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