A boat crew rows 30 km upstream and 50 km downstream, taking exactly 5 hours for each independent passage. Find the speed of the current stream. MCQ with Answer and Explanation
A vehicle covers a path of 360 km at a certain speed. If the speed is increased by 10 km/h, the trip takes exactly 3 hours less. Find the original speed of the vehicle.
A boat goes 6 km upstream and returns back to the starting point in 2 hours. If the speed of the stream is 4 km/h, find the speed of the boat in still water.
Explanation:
Let speed of boat in still water be v. 6 / (v - 4) + 6 / (v + 4) = 2 => 3 / (v - 4) + 3 / (v + 4) = 1 => 3(v + 4 + v - 4) = v^2 - 16 => 6v = v^2 - 16 => v^2 - 6v - 16 = 0. Solving the quadratic equation gives (v - 8)(v + 2) = 0. Since speed must be positive, v = 8 km/h.
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