Sheila can row a boat 2 MPH in still water. How fast is the current of a river if she takes the same length of time to row 4 miles upstream as she does to row 10 miles downstream?

Question

Eva Adamson · Accepted Answer

The speed of current of river is #6/7# miles per hour.

Let the current of water be #x# miles per hour and that Sheila takes #t# hours for each way. As she can row a boat at #2# miles per hour, the speed of boat upstream will be #(2-x)# miles per hour and covers #4# miles hence for upstream we will have #(2-x)xxt=4# or #t=4/(2-x)# and as the speed of boat downstream will be #(2+x)# miles per hour and covers #10# miles hence for upstream we will have #(2+x)xxt=10# or #t=10/(2+x)# Hence #4/(2-x)=10/(2+x)# or #8+4x=20-10x# or #14x=20-8=12# and hence #x=12/14=6/7# and #t=4/(2-6/7)=4/(8/7)=4xx7/8=7/2# hours.

Nathan Axel · Answer

undefined Let $ c $ be the speed of the current.

When rowing upstream, Sheila's effective speed is $ 2 - c $ mph.
When rowing downstream, her effective speed is $ 2 + c $ mph.

Since the time taken for both directions is the same:

$$ \frac{4}{2 - c} = \frac{10}{2 + c} $$

Solve for $ c $:

$$ 4(2 + c) = 10(2 - c) $$

$$ 8 + 4c = 20 - 10c $$

$$ 14c = 12 $$

$$ c = \frac{12}{14} $$

$$ c = \frac{6}{7} $$

So, the speed of the current is $ \frac{6}{7} $ mph.