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

Mathematics

Andreas Rios

21 May, 04:53

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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Joanna Singleton · 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.