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Work Word Problems - Concept
It is possible to solve word problems when two people are doing a work job together by solving systems of equations. To solve a work word problem, multiply the hourly rate of the two people working together times the time spent working to get the total amount of time spent on the job. Knowledge of solving systems of equations is necessary to solve these types of problems.
This problem has to do with mowing lawns, someone who's a contractor of a landscaping business works in a way where they're ordering different people to do different jobs. In this situation Brooks and Jeremy are asked to mow a lawn together. Here's what we're going to do to solve it. Brooks can mow a lawn in 4 hours, Jeremy could mow the same lawn twice as fast. How long would it take them working together? Before we do that let's figure out how fast Jeremy mows, he goes twice as fast as Brooks so if Brooks takes 4 hours then Jeremy is going to take 2 hours right? Does that make sense? Twice as fast means half as much time so Jeremy is going to be 2 hours to do the job by himself. 2 hours alone, okay so what I'm going to be doing is writing fractions for each of these guys and then adding those fractions together to see how quickly they could do this job working together.
Brooks could mow the lawn in 4 hours that means every hour he does 1 fourth of the job does that make sense think about it I'm going to say it again. Brooks could mow the lawn in 4 hours that means he does 1 fourth of the job in every hour. Similarly Jeremy could mow the lawn in 2 hours. So every hour he's going to do half of the job. This represents 1 hour together one half plus one fourth when you find a common denominator instead of one half I'm going to write that as two fourths, one fourth plus 2 fourths equals 3 fourths. What that means is that in 1 hour working together they could do 3 fourths of the jobs. Does that make sense we say it again 1 hour working together, they could do 3 fourths of the job, they're almost done not all the way done.
The way to figure out how long it would take them and to complete the job all the way would be to use the formula fraction they could do together times sum amount of time that they're working equals 1 total job, 1 complete job. All we need to do here is solve for x. Well the way to undo multiplying by a fraction is to either divide by the fraction, or multiply by the reciprocal. I'm going to multiply both sides here by 4 thirds, 4 thirds these cancel out so I'm left with x equals 4 thirds. What that tells me is it would take them 4 thirds of an hour working together in order to mow this lawn.
Before you start doing your homework problems make sure you're not doing the meatball answer, the meatball answer for this kind of a problem would be well if Brooks mows it in 4 hours, Jeremy mows it in 2 hours the meatball would say it takes them 6 hours working together what it does it you guys when they work together it goes faster, that's why again the answer that's faster than either guy working alone. Keep that straight in your head and don't pick the silly multiple choice question. Answer.