A boat can travel 23mph in still water. If it travels 248 miles with the current in the same length of time it travels 120 miles against the current, what is the speed of the current?

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Mathematics

2 March, 13:27

A boat can travel 23mph in still water. If it travels 248 miles with the current in the same length of time it travels 120 miles against the current, what is the speed of the current?

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Chief · Answer 1

Answer: the speed of the current is 8 mph.

Step-by-step explanation:

Let represent the speed of the current

boat can travel 23mph in still water. This means that the total speed with which the boat travelled is (23 + x) mph.

Time = distance/speed

If it travels 248 miles with the current, it means that the time it took the boat to travel with the current is

248 / (23 + x)

in the same length of time it travels 120 miles against the current. This means that the total speed with which the boat travelled is (23 - x) mph. The time it took the boat to travel against the current is

120 / (23 - x)

Since the time is the same, it means that

248 / (23 + x) = 120 / (23 - x)

Cross multiplying, it becomes

248 (23 - x) = 120 (23 + x)

5704 - 248x = 2760 + 120x

120x + 248x = 5704 - 2760

368x = 2944

x = 2944/368

x = 8 mph