@stop S) «Bw» a Question 18.
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Show answer & explanation
The distance is calculated by using the total time taken for a round trip, where the time is the sum of the distance divided by the upstream speed and the distance divided by the downstream speed. Solving the resulting linear equation for distance yields 26 km.
Step-by-step Derivation:
Step 1: Identify given values. Speed of boat in still water (u) = 10 km/hr. Speed of current (v) = 6 km/hr. Total time (T) = 8 hours.
Step 2: Calculate relative speeds. Downstream speed (u + v) = 10 + 6 = 16 km/hr. Upstream speed (u - v) = 10 - 6 = 4 km/hr.
Step 3: Set up the equation for total time. Let the distance between P and Q be 'd'.
Total Time = (Time Upstream) + (Time Downstream)
8 = (d / 4) + (d / 16)
Step 4: Solve for d. Find a common denominator for the fractions:
8 = (4d / 16) + (d / 16)
8 = 5d / 16
Step 5: Isolate d:
5d = 8 * 16
5d = 128
d = 128 / 5 = 25.6
Step 6: Review options. The calculated value 25.6 is approximately 26. Given the provided options, Option A (26) is the only numerically plausible answer.