How to solve a round trip quadratic application?

Question

Okay, I have been working over (well worked over by) this round trip problem. Every approach I have done has yielded either imaginary numbers or cancelled out all my variables. I know the answer is supposed to be 6 mph.

So, here is the problem:

It took a motorboat two hours more to travel 16 miles against the current than it did to travel 16 miles with the current. The rate of the current was 2 miles/hour. Find the rate of the motorboat in calm water.

What I am looking for is a few different strategies for getting to the answer.

Thanks in advance!

Answer 1

Let boat speed in still water be x.

speed upstream = x -2

Time upstream = 16/(x-2)

Similarly time downstream = 16/(x + 2)

Therefore 16/(x-2) = 16/(x +2) + 2

Multiply each term by (x+2)(x-2):

16(x + 2) = 16(x - 2) + 2(x + 2)(x - 2)

16x + 32 = 16x - 32 + 2x² - 8

2x² = 72

x² = 36

x = 6 since we require x > 0

Answer 2

sped up stream = v-2

speed down stream = v+2

average speed = v

distance = 32 miles

time = distance/speed => 2 = 32/v => v =16 mph