   SEARCH HOME Math Central Quandaries & Queries  Subject: linear equation word problem Name: Liz Who are you: Parent This is a word problem in which you are supposed to use a linear system of equations to find the solution or answer to the question they are asking... "A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat in still water is 15 mi/h greater than the speed of the current. Find the speed of the current." Thank you in advance. Hi Liz.

If we call the speed of the boat in still water "s", and the speed of the current "c", then we can write this:

s = 15 + c

This is the first of the linear equations.

Now speed divided by distance equals time, so to go downstream, the boat is going with the current so the total speed is s+c and that means the total time going downstream is (s+c) / 60.

But that is the same amount of time to go 36 miles upstream. So in this case the boat is going against the current so the total speed is s - c. That means the total time going upstream is (s-c) / 36.

Now two things that equal the same third thing must be equal to each other, so since both of these equal the same time, they equal each other:

(s+c) / 60 = (s-c) / 36.

This is the second of the linear equations.

With two linear equations with two unknowns, you can solve for both variables.

Does this help?
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.