Question

A motorboat can maintain a constant speed of 50 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 57 ​minutes; the return trip takes 43 minutes. What is the speed of the​ current?

Answer 1

The speed of the current is 5.75 miles per hour.

Step-by-step explanation:

Let's assume the speed of the current is x miles per hour. When the boat is moving upstream, it is opposing the current, so the effective speed is the difference between the boat's speed and the current's speed. On the upstream trip, the boat takes 57 minutes, which is equivalent to 57/60 = 0.95 hours. The distance traveled upstream is 50 * 0.95 = 47.5 miles. On the return trip downstream, the boat is assisted by the current, so its effective speed is the sum of the boat's speed and the current's speed. The boat takes 43 minutes, which is equivalent to 43/60 = 0.72 hours. The distance traveled downstream is 50 * 0.72 = 36 miles.

Since the distance traveled upstream is equal to the distance traveled downstream, we can set up the equation:

47.5 = 36 + 2x

Simplifying the equation, we find:

2x = 47.5 - 36 = 11.5

x = 11.5/2 = 5.75

The speed of the current is 5.75 miles per hour.

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