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March 3rd, 2012, 09:29 PM   #1
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I am a little Confused.

Hello, I have a problem that I don't know how to solve. Could someone please explain to me what I am suppose to do?

"A car leaves a town traveling at 40 miles per hour. Two hours later a second car leaves the town traveling the same route and overtakes the first car in 5 hours and 20 minutes. How fast was the second car traveling?"
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March 3rd, 2012, 09:43 PM   #2
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Re: I am a little Confused.

Both cars travel the same distance, while the first car travels for 2 hr more. Let t be the time for the second car then t + 2 is the time for the first car. Let v be the speed of the second car which we assume is constant. Using distance equals rate times time, we may state:





We are told giving us:

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March 4th, 2012, 06:47 AM   #3
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The second car made up 80 miles in hours, so its relative velocity was 15 mph. Hence the answer is 55 mph.
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March 8th, 2012, 02:39 PM   #4
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Re: I am a little Confused.

Quote:
Originally Posted by MarkFL
Both cars travel the same distance, while the first car travels for 2 hr more. Let t be the time for the second car then t + 2 is the time for the first car. Let v be the speed of the second car which we assume is constant. Using distance equals rate times time, we may state:





We are told giving us:

Could you explain to me how you got that answer?
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March 8th, 2012, 03:17 PM   #5
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Re: I am a little Confused.

We begin with distance equals rate times time. We let v be the rate of the second car, since we don't know the rate and this is what we're asked to find. If the second car traveled for 5 1/3 hr and the first car left 2 hours before the second then the second car traveled for 7 1/3 hr at 40 mph. Since they both traveled the same distance d we may state:



Now we solve for v:

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March 9th, 2012, 05:52 PM   #6
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Re: I am a little Confused.

Thanks for the explanation. I have another one as well.

How much water needs to be removed from 20 gallons of 30% salt solution to change it to a 40% salt solution?
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March 9th, 2012, 06:20 PM   #7
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Re: I am a little Confused.

30%(Salt) of 20 gallons of solution= 6 gallons
40%(Salt) of x gallons solution= 6 gallons
x=15 gallons.
H20 to be removed=5 gallons.
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March 9th, 2012, 06:24 PM   #8
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Re: I am a little Confused.

I would state 30% of 20 gallons is 40% of how many (x) gallons? Writing this mathematically where 20 and x are in gallons:





Since 20 - 15 = 5, we see 5 gallons of water must be removed.
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March 10th, 2012, 12:26 PM   #9
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Re: I am a little Confused.

Okay, I have another one.

"Suppose that the perimeter of a square equals the perimeter of a rectangle. The width of the rectangle is 9 inches less than twice the side of the square, and the length of the rectangle is 3 inches less then twice the side of the square. Find the dimensions of the square and the rectangle."
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March 10th, 2012, 01:29 PM   #10
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Re: I am a little Confused.

Hi, Siedas. In future please start a new topic for a different (unrelated) question.

Let W be the width of the rectangle. Let L be the length of the rectangle. Let s be the side of the square. From the given information

W = 2s - 9 and L = 2s - 3.

Since perimeter equals 2 times length plus two times width we have

2W + 2L = 4s
2(2s - 9) + 2(2s - 3) = 4s
4s - 18 + 4s - 6 = 4s
4s - 24 = 0
4s = 24
s = 6, so the side of the square is 6, the width of the rectangle is 2(6) - 9 = 3 and the length of the rectangle is 2(6) - 3 = 9.
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