A motorboat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. What is the speed of the stream?
Answer and explanation
Correct answer: D. 6 km/h
- Step 1: Let speed of stream be s km/h. Upstream speed = 18 - s; downstream speed = 18 + s.
- Step 2: Time difference: 24 / (18 - s) - 24 / (18 + s) = 1.
- Step 3: 24 [ (18 + s) - (18 - s) ] / (324 - s^2) = 1 => 24(2s) = 324 - s^2.
- Step 4: s^2 + 48s - 324 = 0 => (s + 54)(s - 6) = 0.
- Step 5: Since speed > 0, s = 6 km/h.
Why not the others: 5 km/h, 4 km/h and 8 km/h do not fit.
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