SOLUTION: A boat can travel 34 mph in still water. If the boat can travel 100 miles with the current in the same time it can travel 80 miles against the current, find the rate of the current

Algebra ->  Equations -> SOLUTION: A boat can travel 34 mph in still water. If the boat can travel 100 miles with the current in the same time it can travel 80 miles against the current, find the rate of the current      Log On


   

Question 1048257: A boat can travel 34 mph in still water. If the boat can travel 100 miles with the current in the same time it can travel 80 miles against the current, find the rate of the current r in miles per hour.
Found 3 solutions by ikleyn, Boreal, addingup:
Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.
A boat can travel 34 mph in still water. If the boat can travel 100 miles with the current in the same time
it can travel 80 miles against the current, find the rate of the current r in miles per hour.
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Your governing equation is

100%2F%2834%2Bv%29 = 80%2F%2834-v%29 

Its       left  side is the time for the boat to travel 100 miles with the current,
while its right side is the time for the boat to travel  80 miles against the current.

To solve the equation, multiply both sides by (34+v)*(34-v). You will get

100*(34-v) = 80*(34+v),  or

3400 - 100v = 2720 + 80v,

3400 - 2720 = 100v + 80v,

680 = 180v

v = 680%2F180 = 3.778.

Answer.  The rate of the current is 3.778 mph  (approximately).



Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
velocity * time=distance; x=current velocity in mph
(34 mph+x)*time=100 miles
time=100/(34+x)
time =(80)/(34-x), going upstream
These times are equal so set the other sides equal to each other.
100/(34+x)=(80)/(34-x)
cross-multiply
2720+80x=3400-100x
180x=680
x=3.78 mph ANSWER (3 7/9 exact)
37.78 mph downstream and takes 2.65 hr.
30.22 mph or 30 7/9 mph upstream and takes 2.65 hrs.

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
d = r*t divide both sides by t
r = d/t
:
Downstream speed per hour: 34+r
Upstream speed per hour: 34-r
According to the formula:
80/34-r = 100/34+r Cross multiply
80(34+r) = 100(34-r)
2720+80r = 3400-100r
80r+100r = 3400-2720
180r = 680
r = 3.78 This is the speed of the current.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Check - In still water, their times would have been:
34+3.78 = 37.78; 100/37.78 = 2.65
34-3.78 = 30.22; 80/30.22 = 2.65
Correct.
John