college algebra

Question

A motor boat traveled 18 miles down a river in 2 hours but took 4.5 hours to return upstream. Find the rate of the motor boat in still water and the rate of the current.

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to find a way to relate the variables algebraically. On this one we have

Downstream Rate: 18 miles / 2 hours = 9 mph

Upstream Rate: 18 miles / 4.5 hours = 4 mph

If you let B represent the boat’s speed and C represent the current speed, that means that our underlying equation here is

(B + C) + (B – C) = 9 + 4

Solving that for B algebraically yields

2B = 13

B = 6.5, meaning that the rate in still water is 6.5 mph

Then

(6.5 + C) = 9

C = 2.5, meaning that the rate of the current is 2.5 mph

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Using the rate equation - D = R*T, we can set up two linear equations. Going downstream, the boat is travel at a rate of B + S mph, where B is the speed of the boat, and S is the speed of the stream. Conversely, the upstream rate is B - S.

The Rate multiplied by the time = the distance, so we can now set up the equations (distances are equal)

Downstream--- (B + S) *2 = 18

Upstream (B - S) * 4.5 = 18

You should be able to solve these two equations for B and S.. I get B = 6.5 mph, and S = 2.5 mph