Word problem on rowing speed

Question

Erin rows a boat downstream for 42 miles. The return trip upstream took 8 hours longer. If the current flows at 2 mph, how fast does Erin row in still water?

Answer 1

Let r = rowing rate (speed) in still water. Then rowing downstream is at net r + 2 mi/hr and upstream is at net r - 2 mi/hr.

Make a "D = R * T" chart:

                    D    R       T

downstream  42  r+2  42/(r+2)

upstream      42  r-2   42/(r-2)

 

Note that the Time column (T) contains a computed expression based on D = R * T, so T = D / R in each case.

 

Now, use the key given fact that downstream time + 8 = upstream time:

42/(r-2) = 42/(r+2) + 8.

This is one equation in one unknown, r.

To solve it, "clear fractions" by multiplying all its terms by the LCD which is (r-2)(r+2) or r² - 4.

You then have a quadratic equation...easy to solve because there's only a squared term, and no r-only term.

 

That's enough from me...you take it from here.  This "DRT CHART" technique is the key to most problems of this type.

 

Ken Seidel           seidel . thailand @ gmail . com