A ship travels downstream for 36 miles and then makes the same return trip upstream. The trip downstream took 3/4 of an hour less then the trip upstream. If the rate of the current is 4mph find the rate of the ship in still water and the time it takes to complete each part of the trip.

Answer 1

speed of ship in still water --- x miles
speed downstream = x+4
speed upstream = x-4

time downstream = 36/(x+4)
time upstream = 36/(x-4)

36/(x-4) - 36/(x+4) = 3/4
multiply by 4(x+4)(x-4)

144(x + 4) - 144(x - 4) = x^2 - 16
expand, arrange as a quadratic, and solve for x

Answer 2

I'm getting x=+-4sqrt73
So how do I get the rate of ship in still water and time it takes to complete each part of trip?

Answer 3

Did I get the wrong answer?

Answer 4

For x

Answer 5

Careless error on my part, that equation should have been
144(x + 4) - 144(x - 4) = 3(x^2 - 16)
144x + 576 - 144x + 576 = 3x^2 - 48
3x^2 = 1200
x^2 = 400
x = ± 20 , came out much nicer!

I had defined x to be speed of the boat in still water, see above
so 20mph is the speed of the boat in still water, one of your questions.

As to the time, we defined them as 36/(x+4) and 36/(x-4)
using my calculator , those turned out as 36/24 hrs and 36/16 hrs
which is 1.5 hrs and 2.25 hrs.
Note the difference in those times is 2.25-1.5 = .75 or 3/4 hour as needed.

(I should have checked my previous answer and that would have shown an error)

Answer 6

No worries. Thanks Reiny!