A motorboat covers a certain distance downstream in a river in 3 hours and returns upstream in 4 hours. If the speed of the river current is 3 km/h, find the speed of the motorboat in still water.
Explanation:
Let speed of boat in still water be v. Downstream speed = v + 3, Upstream speed = v - 3. Distance is same, so 3(v + 3) = 4(v - 3) => 3v + 9 = 4v - 12 => v = 21 km/h.
The speed of a boat in still water is 15 km/h and the speed of the current is 3 km/h. How much distance can the boat cover upstream in exactly 3 hours?
A person has to cover a distance of 160 km. He covers the first half of the distance at 40 km/h. At what speed must he travel the remaining half to make the average speed for the whole journey 50 km/h?
Explanation:
Let the required speed for the second half be x km/h. Using the average speed formula for equal halves: Average Speed = 2v1*v2 / (v1 + v2) => 50 = (2 * 40 * x) / (40 + x) => 50(40 + x) = 80x => 2000 + 50x = 80x => 30x = 2000 => x = 66.67 km/h.
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