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A motorboat maintained a constant speed of 16 miles per hour relative to the water in going 15 miles upstream and then returning. The total time for the trip was 2.0 hours. Use this information to find the speed of the current.

User Mardah
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Final answer:

To find the speed of the current, use the equation 15 / (16 - c) + 15 / (16 + c) = 2.0 and solve for 'c'.

Step-by-step explanation:

To find the speed of the current, let's assume the speed of the current is 'c' miles per hour. When the boat is going upstream, it is moving against the current, so its effective speed is reduced by 'c'. Let 't' be the time it takes for the boat to go upstream.

Since distance = speed x time, we have 15 = (16 - c) x t. Solving for 't', we get t = 15 / (16 - c).

On the return journey downstream, the boat is moving with the current, so its effective speed is increased by 'c'. Let 't' be the time it takes for the boat to go downstream. Using the same reasoning, we have 15 = (16 + c) x t. Solving for 't', we get t = 15 / (16 + c).

Since the total time for the trip is 2.0 hours, we can write the equation: t + t = 2.0. Substituting the values of 't' derived earlier, we have 15 / (16 - c) + 15 / (16 + c) = 2.0. Solve this equation to find the value of 'c', which represents the speed of the current.

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