SOLUTION: Greetings, Francois went 36 miles downstream and returned. The round trip took 5+1/4 (5.25) hours. Find the speed of the boat in still water and the speed of the current if the

Algebra ->  Human-and-algebraic-language -> SOLUTION: Greetings, Francois went 36 miles downstream and returned. The round trip took 5+1/4 (5.25) hours. Find the speed of the boat in still water and the speed of the current if the       Log On


   

Question 318363: Greetings,
Francois went 36 miles downstream and returned. The round trip took 5+1/4 (5.25) hours. Find the speed of the boat in still water and the speed of the current if the speed of the current is 1/7 the speed of the boat.
Thank you in advance for any assistance, have a great week!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Francois went 36 miles downstream and returned.
The round trip took 5+1/4 (5.25) hours. Find the speed of the boat in still
water and the speed of the current if the speed of the current is 1/7 the speed of the boat.
:
Let s = speed of boat in still water
then
1%2F7s = speed of the current
:
The current is added and subtracted from the boat speed so we can say:
8%2F7s = speed downstream
and
6%2F7s = speed upstream
:
Write a time equation, time = dist/speed
36%2F%28%286s%29%2F7%29%29 + 36%2F%28%288s%29%2F7%29%29 = 5.25
invert the dividing fractions and multiply
%287%2836%29%2F6s%29 + %287%2836%29%2F8s%29 = 5.25
:
%28252%2F6s%29 + %28252%2F8s%29 = 5.25
multiply by 24s to eliminate the denominators
4(252) + 3(252) = 5.25(24s)
:
1008 + 756 = 126s
:
s = 1764%2F126
s = 14 mph is the speed of the boat in still water
then
1%2F7*14 = 2 mph is speed of the current
:
:
See if this is true
36/16 + 36/12 =
2.25 + 3 = 5.25 hrs; confirms our solutions