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?
+591 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 $2x\cdot\frac{77}{18x}=\boxed{\frac{77}{9}}$
