A log raft is moving downstream at a speed of 3 km/h. To insure that there are no river jams a supervisor travels along the raft on a motor boat speed of which in still water is 15 km/h. What is the length of the log raft, if it takes the supervisor 16 minutes to travel from one end of the raft to another and back?

Question

Simon

Mathematics

4 February, 23:55

A log raft is moving downstream at a speed of 3 km/h. To insure that there are no river jams a supervisor travels along the raft on a motor boat speed of which in still water is 15 km/h. What is the length of the log raft, if it takes the supervisor 16 minutes to travel from one end of the raft to another and back?

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Tomas Huber · Answer 1

2000 meters

Step-by-step explanation:

When the motorboat is moving downstream, its speed relative to the ground is 18 km/h, so its speed relative to the raft is 15 km/h.

When the motorboat is moving upstream, its speed relative to the ground is 12 km/h, so its speed relative to the raft is again 15 km/h.

Converted to m/min, the relative speed is:

15 km/h * (1000 m/km) * (1 h / 60 min) = 250 m/min

It takes the motorboat 16 minutes to travel to the front of the raft and back. Since the speed is the same in both directions, the motorboat takes 8 minutes to travel the length of the raft.

So the length of the raft is 250*8 = 2000 meters.