A peon walks from P to Q at the rate of 5 kmph. After transacting some business
which occupies him an hour, returns to P by the tramway at the rate of 7 kmph.
He then finds that he has been absent for 2 hours 12 minutes. Find the distance
from P to Q.
Answers
Step-by-step explanation:
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Answer: The distance between P and Q is 3.25 km.
Step-by-step explanation:
Let the distance between P and Q be d.
The time taken for the peon to walk from P to Q at the rate of 5 kmph is given by:
t1 = d/5
After transacting some business for an hour, the peon returns to P by the tramway at the rate of 7 kmph. The time taken for this journey is given by:
t2 = d/7
The total time taken by the peon for the entire journey is 2 hours 12 minutes, which is equivalent to 2 2/5 hours:
t1 + 1 + t2 = 2 2/5
Substituting the expressions for t1 and t2, we get:
d/5 + 1 + d/7 = 2 2/5
Simplifying this equation, we get:
12d/35 + 7/5 = 12/5
Multiplying both sides by 35, we get:
12d + 49 = 84
Solving for d, we get:
d = 3.25 km
Therefore, the distance between P and Q is 3.25 km.
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