Question

Michonne paddles a kayak 14 miles upstream in 3.5 hours. The return trip downstream takes her 2 hours. What is the rate that Michonne paddles in still water? What is the rate of the current?

Answer 1

Michonne paddles at 5.5 mph and the current has a rate of 1.5 mph

1) The way to tackle this question is by considering the speed, distance, and time relation and then setting two equations.

2) Gathering the data:

14 miles upstream in 3.5 hours

downstream in 2 hours

We can write then, the following equation:

`\begin{gathered} S=(d)/(t) \\ S_u=(14)/(3.5)=k-c \\ S_d=(14)/(2)=k+c \\ 4=k-c \\ 7=k+c \\ ------- \\ 11=2k \\ k=5.5mph \\ 2)Subtracting\: both\: equations \\ 4-7=k-c-(k+c) \\ -3=k-c-k-c \\ -3=-2c \\ (-3)/(-2)=(-2c)/(-2) \\ c=1.5\text{mph} \end{gathered}`

Note that on the first part of this solving we wrote the equations considering k the speed of the kayak and c the speed of the current. Then we added both equations to get the value of "k", and then we subtracted to find the value of "c"

3) Thus, the answer is:

Michonne paddles at 5.5 mph and the current has a rate of 1.5 mph