A boat takes 4 hours to go 20 miles upstream. It can go 32 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water. (Hint: Because the current pushes the boat when it is going downstream, the rate of the boat downstream is the sum of the rate of the boat and the rate of the current. The current slows down the boat when it is going upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the current.)

Question

Mathematics

Andrew

1 December, 06:07

A boat takes 4 hours to go 20 miles upstream. It can go 32 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water. (Hint: Because the current pushes the boat when it is going downstream, the rate of the boat downstream is the sum of the rate of the boat and the rate of the current. The current slows down the boat when it is going upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the current.)

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Jaxon Andrews · Answer 1

Let the boat speed in still water be b.

Let the current speed be c.

The speed going upstream is 20/4 = 5 mph.

The speed going downstream is 32/4 = 8 mph.

b - c = 5 ... (1)

b + c = 8 ... (2)

Adding equations (1) and (2) we get:

2b = 13

b = 13/2 = 6.5

Plugging in the value for b into equation (1) we find c = 1.5.

The boat speed in still water is 6.5 mph and the current speed is 1.5 mph.