One day last summer, Jim went kayaking on the Little Susitna River in Alaska. Paddling upstream against the current, he traveled 24 miles in 3 hours. Then he turned around and paddled twice as fast downstream and, with the help of the current, traveled 25 miles in 1 hour. Find the rate of the current.
A) 14 mph
B) 8 mph
C) 11 mph
D) 3 mph

Question

Quizplus · Accepted Answer

The rate of the current can be found by setting up equations based on the given information. Let's denote Jim's kayaking speed in still water as $x$ mph and the speed of the current as $y$ mph. When Jim paddles upstream, his effective speed is $x - y$, and when he paddles downstream, his effective speed is $x + y$. From the given information, we have:1. $24$ miles in $3$ hours upstream: $\frac{24}{3} = x - y = 8$2. $25$ miles in $1$ hour downstream: $25 = 2(x - y) + y = 2x + y$From the first equation, we can express $x$ as $x = 8 + y$. Substituting this into the second equation gives us $25 = 2(8 + y) + y$, which simplifies to $25 = 16 + 3y$, leading to $9 = 3y$, and thus $y = 3$ mph.

One Day Last Summer, Jim Went Kayaking on the Little