Question
A boat can travel 80 km downstream in 4 hours and the
same distance upstream in 8 hours. If the speed of the boat in still water is increased by 50%, how long will it take to travel 120 km downstream at the increased speed?Solution
Let the speed of the boat in still water be B km/h and the speed of the stream be S km/h. From the given data: Downstream speed = B + S = 80 km / 4 hours = 20 km/h. Upstream speed = B - S = 80 km / 8 hours = 10 km/h. Solving these two equations: B + S = 20 and B - S = 10. Adding the two, 2B = 30 → B = 15 km/h. Substituting B = 15 into B + S = 20: S = 5 km/h. Now, the new speed of the boat in still water is 1.5 * 15 = 22.5 km/h. The new downstream speed = 22.5 + 5 = 27.5 km/h. Time to travel 120 km downstream = 120 / 27.5 ≈ 4.36 hours.
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