SOLUTION: Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water.

Algebra ->  Radicals -> SOLUTION: Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water.       Log On


   

Question 217462: Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr.
The speed of the river is 3 mph.
Find the speed of the boat in still water.
:
Let s = speed in still water
then
(s+3) = speed downstream
and
(s-3) = speed upstream
:
write a time equation: Time = dist%2Fspeed
:
Time up + time down = 8 hrs
45%2F%28%28s%2B3%29%29 + 45%2F%28%28s-3%29%29 = 8
Multiply equation by (s-3)(s+3), results
45(s-3) + 45(s+3) = 8(s+3)(s-3)
:
45s - 135 + 45s + 135 = 8(s^2 - 9)
:
90s = 8s^2 - 72
:
8s^2 - 90s - 72 = 0; a quadratic equation
:
Simplify, divide by 2
4s^2 - 45s - 36 = 0
:
Factor
(4s + 3)(s - 12) = 0
:
Positive solution:
s = 12 mph boat speed in still water
;
;
Check solution:
45%2F15 + 45%2F9 = 8
3 + 5 = 8 hrs