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

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(52835)   (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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Your governing equation is = 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 = = 3.778. Answer. The rate of the current is 3.778 mph (approximately).

Answer by Boreal(15235)   (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)   (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

RELATED QUESTIONS
A boat can travel 34 mph in still water. If the boat can travel 100 miles with the... (answered by jorel555,stanbon)
A boat can travel 26 mph in still water. If the boat can travel 100 miles with the... (answered by richwmiller,josgarithmetic,greenestamps,ikleyn)
A boat can travel 28 mph in still water. If the boat can travel 100 miles with the... (answered by stanbon)
A boat can travel 26 mph in still water. If the boat can travel 100 miles with the... (answered by jorel1380,MathTherapy,ikleyn)
A motorboat can travel 20 mph in still water. If the boat can travel 3 miles downstream... (answered by mananth)
A boat can travel 114 miles downstream in the same time that it can travel 24 miles... (answered by josmiceli)
If a boat in a 4 mph current can travel 76 miles downstream in the same time it takes to... (answered by ewatrrr)
a boat travel 6 miles upstream in the same amount of time it can travel 10 miles... (answered by mananth)
a boat can travel 51 mph in still water. if it travels 480 miles with the current in the... (answered by mananth)