SOLUTION: 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

Question 982598: 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 34 miles with the wind, she could go only 18 miles against the wind. What is her normal rowing speed with no wind? Please help!
Found 3 solutions by mananth, josgarithmetic, MathTherapy:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
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 34 miles with the wind, she could go only 18 miles against the wind. What is her normal rowing speed with no wind?
let speed of boat in still water be x
rate of wind =4
with wind rate = x+4
distance with wind = 34 miles
against wind rate = x-4
distance against wind = 18 miles
t = d/r
time against wind = time with wind
34/(x+4) = 18/(x-4)
34(x-4)=18(x+4)
34x-136 =18x+72
34x-18x=72+136
16x=208
x=13 mph

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
r, normal rowing speed
w, the effect of speed of wind
t, amount of time for given paths
u, distance WITH the wind
v, distance AGAINST the wind
-
Unknowns assumed to be t and r.
GIVEN:

___________________rate____________time___________distance
WITHWND____________r+w______________t______________u
AGAINSTWND_________r-w______________t______________v

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

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 34 miles with the wind, she could go only 18 miles against the wind. What is her normal rowing speed with no wind? Please help!

Let rowing speed of boat with no wind, be S
Then rowing speed with wind = S + 4, and rowing speed against wind = S - 4
Time taken to row 34 miles, with wind:
Time taken to row 18 miles, against wind:
Since times are the same, we get:

34(S - 4) = 18(S + 4) ------- Cross-multiplying
34S - 136 = 18S + 72
34S - 18S = 72 + 136
16S = 208
S, or speed with no wind = , or mph
RELATED QUESTIONS
On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing... (answered by josgarithmetic)
On a particular day, the wind added 5 miles per hour to Jaime's rate when she was rowing... (answered by Theo)
On a particular day, the wind added 5 miles per hour to Jaime's rate when she was rowing... (answered by macston)
On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was... (answered by greenestamps,ikleyn)
On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was... (answered by Alan3354)
On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was... (answered by josgarithmetic)
On a particular day, the wind added 5 miles per hour to Alfonso's rate when he was... (answered by josgarithmetic)
On a particular day, the wind added 3 miles per hour to Alfonso's rate when he was... (answered by josgarithmetic)
On a particular day, the wind added 3 miles per hour to Alfonso's rate when he was... (answered by MathLover1,jim_thompson5910)