The steamboat traveled down the Ohio River at 22 mph and upstream at 14 mph. What was the steamboat's upstream travel time if it was 4 hours more than the time required to travel the same distance downstream?

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High School

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Answer :

parthshukla4090 parthshukla4090 · Answer 1 · 2024-01-28T20:40:24-05:00

The distance traveled by the steamboat is 154 miles, and the upstream travel time is 11 hours.

Let's assume the distance traveled by the steamboat is D.

The downstream speed of the steamboat is 22 mph, so the downstream travel time can be calculated as D/22.

The upstream speed of the steamboat is 14 mph, so the upstream travel time can be calculated as D/14.

According to the given information, the upstream travel time is 4 hours more than the downstream travel time.

So we can set up the equation:

D/14 = D/22 + 4

To solve this equation, we can multiply both sides by the least common multiple (LCM) of 14 and 22, which is 154:

11D = 7D + 616

Subtracting 7D from both sides:

4D = 616

Dividing both sides by 4:

D = 154

Therefore, the distance traveled by the steamboat is 154 miles.

To find the upstream travel time, we substitute this distance into the upstream travel time formula:

Upstream travel time = Distance / Upstream speed = 154 / 14 = 11 hours

Therefore, the steamboat's upstream travel time was 11 hours.

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