SOLUTION: A boat can go 63 mph in still water. It takes as long to go 120 miles upstream as it does to go 150 miles downstream. What is the current?

Algebra ->  Expressions-with-variables -> SOLUTION: A boat can go 63 mph in still water. It takes as long to go 120 miles upstream as it does to go 150 miles downstream. What is the current?      Log On


   

Question 462476: A boat can go 63 mph in still water. It takes as long to go 120 miles upstream as it does to go 150 miles downstream. What is the current?
Found 2 solutions by rwm, josmiceli:
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
(63+x)*t=150
t=150/(63+x)
(63-x)*t=120
t=120/(63-x)
150/(63+x)=120/(63-x)
120*(63+x)=150*(63-x)
x=7 mph current
BTW t=15/7
(63+7)*15/7=150
10*15=150
ok
(63-7)*15/7=120
56/7*15=120
8*15=120
ok



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = speed of current
Let +t+ = time to go either upstream or downstream
given:
Speed in still water = +63+ mi/hr
Going upstream, speed = +63+-+c+
Going downstream, speed = +63+%2B+c+
Upstream:
(1) +120+=+%2863+-+c%29%2At+
Downstream:
(2) +150+=+%2863+%2B+c%29%2At+
Add the equations
+120+%2B+150+=+%2863-c%29%2At+%2B+%2863%2Bc%29%2At+
+270+=+63t+-+c%2At+%2B+63t+%2B+c%2At+
+270+=+126t+
+t+=+2.143+ hrs
Substitute in (2)
(2) +150+=+%2863+%2B+c%29%2A2.143+
(2) +150+=+135+%2B+2.143c+
(2) +2.143c+=+15+
(2) +c+=+7+
The speed of the current is 7 mi/hr
check:
(1) +120+=+%2863+-+7%29%2A2.143+
(1) +120+=+56%2A2.143+
(1) +120+=+120.008+ (rounding off error)
OK