Upstream and Downstream Rate Question to Determine Total Time of Boat Trip

Question

You are wakeboarding on a river. You travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to a

dock. The boat travels 2 miles per hour during the entire trip, and the river current is 3 miles per hour.

a. Write an expression that represents the total time of the trip. Write your answer in simplified form.

b. How long will the trip take when the speed of the boat is 18 miles per hour?

Answer 1

You must first account for the downstream and upstream trips using their distances and rates with regard to the boat's speed (x miles per hour).

We must use the rate formula: D (distance) = Rate x Time

Downstream Trip: Distance = 2 miles, Rate = x + 3 (since you are adding the rate of the water current to the boat's rate)

Upstream Trip: Distance = 3 miles, Rate = x - 3 (since the boat is traveling against the rate of the water current)

To calculate the total time, you must use the rate formula to solve for T, which is D/R or distance/rate:

T (downstream) = 2 / (x + 3)

T (upstream) = 3 / (x - 3)

Total time = 2/(x+3) + 3/(x-3)

To simplify the expression for total time, you must find a common denominator: 2(x-3) + 3(x+3) / (x+3)(x-3) = 5x+3 / (x+3)(x-3) ANSWER to Part A

__________________

ANSWER to Part B:

Plug in 18 miles per hour for x in the expression 5x+3 / (x+3)(x-3) = 5(18) + 3 / (18+3)(18-3) = 0.2952380952 hours

Convert the hours to minutes to get the total time to the nearest tenth of a minute: (0.2952380952 hrs)(60 min/hr) = 17.7. minutes