rational equation??

Question

On a particular day, the wind added 2 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 2 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 51 miles against the wind.What is her normal rowing speed with no wind?

Answer 1

Hi Abe,

Look at the difference in miles.  63-51=12 miles.  The increase or decrease is the same 2 mi/hr so she gained 6 miles with the wind and lost 6 miles against the wind.  Both are 3 hr trips.  Without the wind she would have gone 57 miles (adding or removing 6 miles) in 3 hours.  That is 19 mi/hr as her base rate without wind.

time = (63-51)/2      /2            = 3 hrs

               miles       hrs/miles

 

base rate = (63+51)/2    /3      = 19 mi/hr

                     miles        hrs

 

It is essential to look at the units when analyzing a word problem to convert it into equations.

Answer 2

19 miles per hour

 

Answer 3

Since she adds two miles per hour with wind, and loses two mph against the wind, her "typical" speed would be the average of 51 and 63, which is 57.  The distance between 57 and 63 (6) divided by 2 tells you the number of hours traveled (3).  From there, you can find the MPH by dividing by 3.  57/3=19, so her windless speed is 19 mph.