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Another little help please

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by fambrini » Tue Oct 11, 2016 5:18 pm
A conveyer belt moves grain at the rate of 2 tons in 5 minutes and a second conveyer belt moves grain at the rate of 3 tons in 7 minutes. How many minutes will it take to move 20 tons of grain using both conveyer belts?

A) 12
B) 16 4/7
C) 18 3/6
D) 21
E) 24 4/29

OA: E
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by [email protected] » Tue Oct 11, 2016 5:50 pm
Hi fambrini,

This question is ultimately about converting two rates into a combined rate; you can organize the information in a couple of different ways.

2 tons/5 minutes = 14 tons/35 minutes
3 tons/7 minutes = 15 tons/35 minutes

Combined, 29 tons would be moved in 35 minutes. Since we're asked to figure out how long it would take 20 tons to be moved, we can set up a ratio:

29/35 = 20/X

And then cross-multiply:

29X = (35)(20)
29X = 700
X = 700/29
X = 24 4/29

Final Answer: E

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by DavidG@VeritasPrep » Wed Oct 12, 2016 10:45 am
fambrini wrote:A conveyer belt moves grain at the rate of 2 tons in 5 minutes and a second conveyer belt moves grain at the rate of 3 tons in 7 minutes. How many minutes will it take to move 20 tons of grain using both conveyer belts?

A) 12
B) 16 4/7
C) 18 3/6
D) 21
E) 24 4/29

OA: E
Another way to think about it:

A and B have rates that are awfully close. A: 2/5 = .4. B: 3/7 = about .43 (You just need to see that 3/7 is a little more than .4)

If A can move grain at a rate of 2 tons in 5 minutes, it could do 20 tons in 50 minutes.
Two A's working together would do 20 tons in half the time, or 25 minutes. Because A is working with B, and B is slightly faster than A, the two together would do the job in slightly less than 25 minutes. Answer is E
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by Matt@VeritasPrep » Fri Oct 14, 2016 1:15 am
Let's get them in the same ratio, like tons per minute:

Belt A: 2/5 of a ton per minute
Belt B: 3/7 of a ton per minute

Then, since they're working together, we'll add them up:

Belts A + B = (2/5 + 3/7) of a ton per minute = 29/35 of a ton per minute

Now we just use Work = Rate * Time, with Work = 20 and R = 29/35:

20 = (29/35) * T

20*35/29 = T

Since the 29 won't cancel from the numerator, we need a 29 in the answer, so only E works!
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by Matt@VeritasPrep » Fri Oct 14, 2016 1:17 am
You could also cheat a bit with the answers, as David suggests.

Suppose we start with E and work our way down.

In 25 minutes, Belt A will move 2 tons * 5 = 10 tons.

In 25 minutes, Belt B will move 3 tons * 25/7 ≈ 11 tons.

This is really close to 20 tons, so it should take just a hair less than 25 minutes, making E the choice.
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by Scott@TargetTestPrep » Fri Oct 14, 2016 5:46 am
fambrini wrote:A conveyer belt moves grain at the rate of 2 tons in 5 minutes and a second conveyer belt moves grain at the rate of 3 tons in 7 minutes. How many minutes will it take to move 20 tons of grain using both conveyer belts?

A) 12
B) 16 4/7
C) 18 3/6
D) 21
E) 24 4/29
We can classify this problem as a "combined worker" problem. To solve this type of problem we should use the formula:

Work (done by machine 1) + Work (done by machine 2) = Total Work Completed

It takes one conveyer belt 5 minutes to move 2 tons of grain, so the rate of conveyer belt 1 is 2/5. It takes the second conveyer belt 7 minutes to move 3 tons of grain, so the rate of conveyer belt 2 one is 3/7.

Since we know they are both working together to complete the job, we can label this unknown time as "t" for each conveyer belt during the time that both machines are working together. Since rate x time = work, we can multiply to get the work completed for each machine.

Work completed by conveyer belt 1 = (2/5)t

Work completed by conveyer belt 2 = (3/7)t

Finally, we can plug our two work values into the combined work formula to determine t. Since 20 tons of grain are moved, the total work completed is 20.

Work (done by conveyer belt 1) + Work (done by conveyer belt 2) = Total Work Completed

(2/5)t + (3/7)t = 20

Multiplying the entire equation by 35 gives us:

14t + 15t = 700

29t = 700

t = 700/29 = 24 4/29

Answer is E

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