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

Answer 1

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