It would take Tom 10 hours to paint the fence around his backyard by himself. After Tom has been painting for 2 hours, Jerry comes to help him and together they finish painting the fence in 3 more hours. How many hours would it have taken Jerry to paint the fence himself?
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There is a general class of problems that are called "rate time" problems.
RT=D or Rate times Time = Distance.
Sometimes they are
RT = RT
or RT + RT = D or RT-RT = D.
This is just a form of that.
Tom paints a fence at a rate of 1 every 10 hours. so he paints at a rate of .1/hour
0.1(5) (tom painted for 5 hours) + Jerry worked with him 3x at an unknown rate for three of those 5 hours
=1 and they completed 1 fence
0.1(5)+3x=1
Jerry paints at a rate of 1/6 fence/hour
So he will paint the fence by himself in six hours.
Got it? Just think of this sort of problem as a rate time = distance. In this case there was one job, two workers, and different times, so it is RT + rt = d
RT=D or Rate times Time = Distance.
Sometimes they are
RT = RT
or RT + RT = D or RT-RT = D.
This is just a form of that.
Tom paints a fence at a rate of 1 every 10 hours. so he paints at a rate of .1/hour
0.1(5) (tom painted for 5 hours) + Jerry worked with him 3x at an unknown rate for three of those 5 hours
=1 and they completed 1 fence
0.1(5)+3x=1
Jerry paints at a rate of 1/6 fence/hour
So he will paint the fence by himself in six hours.
Got it? Just think of this sort of problem as a rate time = distance. In this case there was one job, two workers, and different times, so it is RT + rt = d
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I just solved the equation I wrote for x. You can download Microsoft Math, paste my equation into it, and the hit enter. It will solve it for the only variable, x. You can then click on show steps, and it will show you the steps. This works for any simple equation, and now you know how to fish.
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You can download Microsoft Math at my reference. It is free to use and download, not even ads. But it is not "free software" in the technical sense because the source is not released and people are not free to mod it. It can do a boatload of algebra. The only real thing left is to set up word probs.
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ohh got it, okay thanks!
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tom has painted 20% before jerry got there
therefore in the 3hours that jerry was there tom painted another 30%
jerry painted 50% in 3hours
therefor jerry would have painted it in 6hours
im no good with algebra so i cant put this into a algebraic solution but that is the answer.
therefore in the 3hours that jerry was there tom painted another 30%
jerry painted 50% in 3hours
therefor jerry would have painted it in 6hours
im no good with algebra so i cant put this into a algebraic solution but that is the answer.
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Let j = time required for Jerry alone
5/10 + 3/j = 1
2j + 10 = 10j
10 = 8j
5/4 = j
It would take Jerry 1 hr 15 min by himself.
5/10 + 3/j = 1
2j + 10 = 10j
10 = 8j
5/4 = j
It would take Jerry 1 hr 15 min by himself.