SOLUTION: Alma rows a boat downstream for 130 miles. The return trip upstream took 16 hours longer. If the current flows at 4 mph, how fast does Alma row in still water?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Alma rows a boat downstream for 130 miles. The return trip upstream took 16 hours longer. If the current flows at 4 mph, how fast does Alma row in still water?      Log On


   

Question 1140034: Alma rows a boat downstream for 130 miles. The return trip upstream took 16 hours longer. If the current flows at 4 mph, how fast does Alma row in still water?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
r, speed in still water
                  SPEED        TIME          DISTANCE

downstream          r+4         130/(r+4)     130

upstream            r-4         130/(r-4)     130

difference                          16

130%2F%28r-4%29-130%2F%28r%2B4%29=16
-
65%2F%28r-4%29-65%2F%28r%2B4%29=8
65%28r%2B4%29-65%28r-4%29=8%28r%5E2-16%29
65r%2B65%2A4-65r%2B65%2A4=8r%5E2-8%2A16
8%2A65=8r%5E2-8%2A16
65=r%5E2-16
r%5E2=49
highlight%28r=7%29

Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the Alma's rowing speed in still water.


Then the speed downstream is (x+4) mph, and the speed upstream is  (x-4) mph.


The time downstream  is  130%2F%28x%2B4%29 hours; the time upstream is  130%2F%28x-4%29 hours.


The "time" equation is


130%2F%28x-4%29 - 130%2F%28x%2B4%29 = 16   hours.


Solve it for x and get the answer.


Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


Of course you should know how to set up and solve the problem using formal algebra, as shown by both the other tutors.

But if you just need the answer as quickly as possible, trial and error with some mental arithmetic is something you should try.

Guessing that the numbers in the problem are whole numbers, look for two ways to express the 130 miles as the product of a time and a speed that satisfy the conditions of the problem.

Since the rate of the current is 4mph, the difference in the upstream and downstream rates is 8mph. And we know the difference in the two times is 16 hours.

The two most obvious pairs of whole numbers with a product of 130 are 13*10 and 26*5.

And they work: the difference between 13 and 5 is 8; the difference between 10 and 26 is 16.

So the downstream trip was 10 hours at 13mph; the upstream trip was 26 hours at 5mph.

Finally, since the upstream and downstream speeds were 5mph and 13mph, her speed in still water is 9mph.