SOLUTION: A boat takes 1.5 hour to go 12 miles upstream against the current. It can go 24 miles downstream with the current in the same amount of time. Find the speed of the current and the

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A boat takes 1.5 hour to go 12 miles upstream against the current. It can go 24 miles downstream with the current in the same amount of time. Find the speed of the current and the       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 819775: A boat takes 1.5 hour to go 12 miles upstream against the current. It can go 24 miles downstream with the current in the same amount of time. Find the speed of the current and the speed of the boat in still water.
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
r, speed of boat without any current
c, speed of current

WhichWay______speed_________time________________distance
Up____________r-c___________12/(r-c)_____________12
Down__________r+c___________24/(r+c)_____________24

The times are equal, according to given description.
We also know r-c=1.5, also based on given description.

We have two equations:
highlight_green%28r-c=1.5%29 and highlight_green%2812%2F%28r-c%29=24%2F%28r%2Bc%29%29
Solve for r and c.

Actually there is something else you could do.
Knowing r-c=1.5, use this for the upstream information, the time is 12%2F%281.5%29=8 hours. This is also supposed to be the downstream time for the 24 mile distance.
Now you could say 12%2F%28r-c%29=8 and 24%2F%28r%2Bc%29=8 and solve these two equations for r and c.