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# help algebra

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If Judy rows at the rate of 7 mph against the current, and 11mph with the current, what is the average speed of her trip if she goes the same distance in both directions?

Aug 24, 2021

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Lets say she rows x miles in each direction.

When she rows against the current, she travels for $\frac{x}7$ hours.

When she rows with the current, she travels for $\frac{x}{11}$ hours.

In total, she rows $\frac{11x+7x}{77}=\frac{18x}{77}$ hours.

She rows 2x miles in $\frac{18x}{77}$ hours, so the average speed Judy rows is $2x\cdot\frac{77}{18x}=\boxed{\frac{77}{9}}$

Aug 24, 2021