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 42 miles with the wind, she could go only 34 miles against the wind. what is her normal rowing speed with no wind?

Let the normal rowing speed with no wind = x mph

So , speed with the wind = (x+2) mph

and speed against the wind = (x-2) mph

It means

Time taken in going with the wind = Distance/speed = 42/(x+2) hours

and

Time taken in going against the wind = 34/(x-2) hours

And Both times are same , according to the question

So

42/(x+2) = 34/(x-2)

On cross multiplying, we get

42(x-2) = 34(x+2)

42x-84 = 34x+68

Add 90 to both sides

42x -84 + 84 = 34x + 68 +84

42x = 34x +152

Subtract 34x from both sides

42x - 34x = 34x - 34x +152

8x = 152

Divide both sides by 8

x= 19

That implies

The normal rowing speed = 19 Miles per hour