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Question 1163561: 1. Celestine Rides her power boat up and down the Merloquet river. The water in the river flows at 6 miles per hour. Celestine then takes 5 hours longer to travel 360 miles against the current than she does to travel 360 miles along with the current. Write a model that shows how to get the speed of Celestine's boat in still water.
2. Leticia got 80%, 65% and 70% on his three long exams in Mathematics. For her to pass this grade's component, she must obtain an average at least 75% in all his long exams. How much should she obtain on the last long exam to earn at least 75%?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! --------------------------------
Celestine Rides her power boat up and down the Merloquet river. The water in the river flows at 6 miles per hour. Celestine then takes 5 hours longer to travel 360 miles against the current than she does to travel 360 miles along with the current. Write a model that shows how to get the speed of Celestine's boat in still water.
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SPEED TIME DISTANCE
AGAINST r-6 360/(r-6) 360
WITH r+6 360/(r+6) 360
DIFFERENCE 5
Does this help you see what to do?
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
1. the boat problem....
Let the boat speed be x. Then her speed against the current is (x-6)mph, and her speed with the current is (x+6)mph.
Then the time to go 360 miles against the current is 360/(x-6) and the time to go 360 miles with the current is 360/(x+6).
The trip against the current takes 5 hours longer than the trip with the current:
The problem says "write a model..."; it does not say to solve the problem. So I leave that part of my response there.
If indeed you need to solve the problem, solving the problem algebraically, by solving that equation, is relatively easy.
If your mental math is good, you might be able to find the solution faster by trial and error. (And even if you aren't successful, you will get some good brain exercise.)
It is highly likely, since the difference in times is exactly 5 hours, that the times for the two trips, and the speed of the boat in still water, are all positive integers.
So make a list of integer times greater than 5 hours and the corresponding speeds required to go 360 miles in each number of hours. You are looking for two times that differ by 5 hours, with the corresponding speeds differing by 12mph (the difference between (x+6) and (x-6)).
hours speed
---------------
6 60
8 45
9 40
10 36
12 30
15 24
18 20
... ...
The only two times that differ by 5 hours are 10 and 15; and the corresponding speeds, 36 and 24, differ by 12, as required.
So she went 15 hours at 24mph against the current and 10 hours at 36mph with the current.
So the speed of her boat in still water is 24+6 = 30mph, or 36-6 = 30mph.
2. The test average problem....
Formally, if the score on the last exam is x, then the average of 80, 65, 70, and x must be 75 (or greater). To avoid confusion, find the score required to achieve an average of EXACTLY 75:
That equation is easily solved using basic algebra.
Again, common sense and a bit of easy mental arithmetic can solve this problem quickly.
The average of the first and third tests (80 and 70) is exactly the desired 75 average. The other test, 65, is 10 points below the desired average; therefore, the last test must be 10 points above the desired average.
ANSWER: Her score on the last test must be at least 75+10 = 85 to obtain an overall average of 75.
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