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 60 miles with the wind, she could go only 48 miles against the wind.What is her normal rowing speed with no wind?

Answer 1

`t=(d)/(v)`
t - time, d - distance, v - speed

Let x be Jaime's normal rowing speed.

The wind adds 2 miles per hour to her speed when she is rowing with the wind - so her speed is x+2, and she can row 60 miles at that speed in time t.

`t=(60)/(x+2)`

The wind subtracts 2 miles per hour from her speed when she is rowing against the wind - so her speed is x-2, and she can row 48 miles at that speed in the same time t.

`t=(48)/(x-2)`

Set the expressions for t equal to each other:

`(60)/(x+2)=(48)/(x-2) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{cross multiply} \\ 60(x-2)=48(x+2) \ \ \ \ |/ 12 \\ 5(x-2)=4(x+2) \\ 5x-10=4x+8 \\ 5x-4x=8+10 \\ x=18`

Jaime's normal rowing speed is 18 miles per hour.