A person went from P to Q, at an average speed of a km/hr, from Q to R at an average speed of b km/hr, and from R to S at an average speed of the c km/hr. If PQ = QR = RS, then the average speed of the person for traveling from P to S was
Question
A person went from P to Q, at an average speed of a km/hr, from Q to R at an average speed of b km/hr, and from R to S at an average speed of the c km/hr. If PQ = QR = RS, then the average speed of the person for traveling from P to S was
Solution
The average speed of a journey is calculated by dividing the total distance by the total time taken.
In this case, the total distance from P to S is 3PQ (since PQ = QR = RS).
The time taken to travel from P to Q is PQ/a, from Q to R is QR/b, and from R to S is RS/c.
So, the total time taken for the journey from P to S is PQ/a + QR/b + RS/c.
Since PQ = QR = RS, we can simplify this to PQ(1/a + 1/b + 1/c).
Therefore, the average speed for the journey from P to S is the total distance divided by the total time, which is 3PQ / [PQ(1/a + 1/b + 1/c)].
This simplifies to 3 / (1/a + 1/b + 1/c) km/hr.
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