SOLUTION: A boat can travel 26 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
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Question 1093565: A boat can travel 26 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. (Enter an exact number as an integer, fraction, or decimal.)
r = _ mph Found 4 solutions by richwmiller, josgarithmetic, greenestamps, ikleyn:Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website! I used c for current.
r*t=d
(26-c)*t=80
26*t-c*t=80
(26+c)*t=100
26*t-c*t=80
26*t+c*t=100
add
52t=180
t=180/52
t=3.46153846 hr
26*3.46153846+c*3.46153846=100
90.0+c*3.46153846=100
c*3.46153846=10.0
c=10.0/3.46153846
c=2.88888889 mph current
check
(26+c)*t=100
(26+2.88888889)*3.46153846=100
(28.8888889)*3.46153846=100
100.0=100
(26-c)*t=80
(26-2.88888889)*3.46153846=80
(23.1111111)*3.46153846=80
80.0=80
ok
You can put this solution on YOUR website! You might want to arrange the data from the description as a table.
c, speed of the current
t, the equal time both directions taken
SPEED TIME DISTANCE
WITH CURRENT 26+c t 100
AGAINST CURRENT 26-c t 80
WITH CURRENT will give and AGAINST will give . Both expressions of t are equal:
You can put this solution on YOUR website! Both earlier responses show the same correct answer, but the formal algebra is a lot of work. I like methods of solving problems that get me to the answer with as little work as possible. Here is what I would do with this problem.
The distances covered in equal amounts of time with and against the current are in the ratio 100:80, or 5:4. That means that must be the ratio of the speeds with and against the current.
You can put this solution on YOUR website! .
A boat can travel 26 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.
(Enter an exact number as an integer, fraction, or decimal.)
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It is classic Travel and Distance problem, at it deserves the full straightforward solution would be presented.
Let "r" be the current rate in miles per hour.
Then the boat's effective rate traveling downstream is (26+r) mph (relative to the river's bank).
The boat relative rate rate traveling upstream is (26-r) mph.
The time to travel 100 miles downstream is hours.
The time to travel 80 miles upstream is hours.
These amounts of time are the same, which gives you an equation
= .
It is so called "time" equation. //Notice that the time equation was written incorrectly
in the @josgarithmetic solution.
Cancel the factor of 20 in both sides; then cross-multiply. You will get
5*(26-r) = 4*(26+r) ====>
130 - 5r = 104 + 4r ====> 130 - 104 = 5r + 4r ====> 9r = 26 ====> r = mph = mph.
Answer. The current rate is mph = mph.
After reading this solution you will have a solid base and knowledge on how to solve and how to present it.
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