SOLUTION: carmines boat has a top speed of 9 mph in still water. while traveling on a river at TopSpeed she went 10 miles upstream in the same amount of time she went 20 miles downstream. Fi

Algebra ->  Length-and-distance -> SOLUTION: carmines boat has a top speed of 9 mph in still water. while traveling on a river at TopSpeed she went 10 miles upstream in the same amount of time she went 20 miles downstream. Fi      Log On


   

Question 1047181: carmines boat has a top speed of 9 mph in still water. while traveling on a river at TopSpeed she went 10 miles upstream in the same amount of time she went 20 miles downstream. Find the rate of the river current.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the rate of the current
Let +t+ = time in hrs for both trips
------------------
Equation for going upstream:
(1) +10+=+%28+9+-+c+%29%2At+
Equation for going downstream:
(2) +20+=+%28+9+%2B+c+%29%2At+
------------------------------
(1) +t+=+10%2F%28+9+-+c+%29+
Plug (1) into (2)
(2) +20+=+%28+9+%2B+c+%29%2A%28+10%2F%28+9+-+c+%29+%29+
(2) +20%2A%28+9+-+c+%29+=+10%2A%28+9+%2B+c+%29+
(2) +180+-+20c+=+90+%2B+10c+
(2) +30c+=+90+
92) +c+=+3+
The rate of the current is 3 mi/hr
------------------------------
check:
(1) +10+=+%28+9+-+c+%29%2At+
(1) +10+=+%28+9+-+3+%29%2At+
(1) +10+=+6t+
(1) +t+=+5%2F3+
and
(2) +20+=+%28+9+%2B+c+%29%2At+
(2) +20+=+%28+9+%2B+3+%29%2At+
(2) +20+=+12t+
(2) +t+=+5%2F3+
OK