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 54 miles with the wind, she could go only 30 miles against the wind. What is her normal rowing speed with no wind?

Nice so

remember

t=d/s

a (b+c) = ab+ac

time=distance/speed

lets say s=jamie's normal speed

speed agains wind=s-4

speed with wind=s+4

30 miles is agains wind

distance is 54 with wind

t=d/s

t=30 / (s-4)

t=54 / (s+4)

since they are both equal to t, set them equal to each other

30 / (s-4) = 54 / (s+4)

multipliy both sides by (s+4) (s-4)

30 (s+4) = 54 (s-4)

distribute

30s+120=54s-216

subtract 30s from both sides

120=24s-216

add 216 to both sides

336=24s

divide both sides by 24

14=s

answer is 14 miles per hour without wind