Word problem help

Question

On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her return trip.  Jaime found that in the same amount of time she could row 63 miles with the wind, she could go only 39 miles against the wind.  What is her normal rowing speed with no wind?

Answer 1

Remember that distance = rate × time. Let r = Jaime's rowing speed with no wind. We'll write two equations:

 

 

 

WITH THE WIND

 

Let t = time. Rate is r + 4, her normal rowing speed plus the speed of the wind. So:

 

63 = t(r + 4)

 

 

 

AGAINST THE WIND

 

Let t = time, since she rowed for the same amount of time. Rate is r - 4, her normal rowing speed minus the speed of the wind. So:

 

39 = t(r - 4)

 

 

 

Now you have a system of equations:

 

63 = t(r + 4)

39 = t(r - 4)

 

Solve each for t, then set them equal to each other and solve for r:

 

63 / (r+4) = t

39 / (r-4) = t

 

63 / (r+4) = 39 / (r-4)

63r - 252 = 39r + 156

24r = 408

r = 17

 

Jaime's normal rowing speed is r = 17 MPH.