Question : Two 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 six hours. If the former train travels 8 km/h faster than the other, the speed of the train from Q is:
Option 1: $12\frac{5}{6}$ km/h
Option 2: $10\frac{5}{6}$ km/h
Option 3: $9\frac{1}{2}$ km/h
Option 4: $8\frac{1}{2}$ km/h
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Correct Answer: $9\frac{1}{2}$ km/h
Solution :
Given: Two 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 six hours and the former train travels 8 km/h faster than the other.
Let the speed of the train from Q be x km/h.
Then the speed of the train from P is (x + 8) km/h.
Now in 6 hours the train from Q to P travels 6x km and 6(x + 8) km respectively.
Here, 6x + 6(x + 8) = 162
⇒ 12x = 162 – 48
⇒ x = $\frac{114}{12} = 9\frac{1}{2}$
Hence, the correct answer is $9\frac{1}{2}$ km/h.
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