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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

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