Question

An otter is floating down a river. The river has a current speed of 1 mile per hour (mph), and so the otter is also moving at a speed of 1 mph. At some point, the otter passes by a team of rowers rowing against the current, in the opposite direction of the otter. At some point, the rowers turn around and start rowing downstream. Four hours after passing each other the first time, the rowers and the otter pass each other again at the boathouse.

In still water, the rowers can row at a speed of 4 mph. How many miles did the rowers travel upstream between the time they first passed the otter and the time they turned around?

Answer 1

The rowers traveled 7.5 miles upstream against the current before turning around to meet the otter again.

Step-by-step explanation:

The student's question asks how many miles the rowers travel upstream against the current before turning around if they pass the otter again at the boathouse four hours later. We know that the river's current is 1 mph and the rowers' speed in still water is 4 mph. When the rowers travel upstream against the current, their effective speed is 3 mph (4 mph - 1 mph current). After turning around, their effective speed downstream is 5 mph (4 mph + 1 mph current).

Let's denote the distance the rowers travel upstream as D miles. They take D/3 hours to travel this distance upstream, and they'll take D/5 hours to travel the same distance downstream. Given that they meet the otter again after 4 hours, we can set up the equation:

• (D/3) + (D/5) = 4

Solving for D gives us:

• 5D + 3D = 60
• 8D = 60
• D = 60/8
• D = 7.5 miles

The rowers traveled 7.5 miles upstream before turning around.