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Select the correct answerTwo places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8 km/hour faster than the other, then speed of train from Q is?Options12 5/6 km/hour9 1/2 km/hour8 1/2 km/hour10 5/6 km/hour

Question

Select the correct answerTwo places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8 km/hour faster than the other, then speed of train from Q is?Options12 5/6 km/hour9 1/2 km/hour8 1/2 km/hour10 5/6 km/hour

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Solution

Let's solve this step by step:

  1. The two trains meet after 6 hours, so combined they cover 162 km in 6 hours. Therefore, their combined speed is 162 km / 6 hours = 27 km/hour.

  2. Let's denote the speed of the train from Q as x km/hour. Then the speed of the train from P is x + 8 km/hour.

  3. Since the combined speed of the two trains is 27 km/hour, we can write the equation: x + (x + 8) = 27.

  4. Solving this equation gives: 2x + 8 = 27, then 2x = 27 - 8, so 2x = 19, and finally x = 19 / 2 = 9.5 km/hour.

So, the speed of the train from Q is 9.5 km/hour, which corresponds to option 9 1/2 km/hour.

This problem has been solved

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