MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
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MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
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 is what we’re going to do to solve it.
Brooks can mow a lawn in 4 hours. Jeremy can 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 hour 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 ever hour he does ¼ of the job, does that make sense? Think about it I’ll just say it again. Brooks could mow the lawn in 4 hours. That means he does ¼ 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.1/2 plus 1/4 when you find the common denominator instead of 1/2, I’m going to write that as 2/4. ¼ plus 2/4, equals 3/4. What that means is that in 1 hour working together; they could do ¾ of the job. Does that make sense? Let me say it again. 1 hour of working together they could do ¾ of the job. They’re almost done, not all the way done.
The way to figure out how long it would take them 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 one total job, one 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 of multiply by the reciprocal.
I’m going to multiply both sides here by 4/3, 4/3, 4/3, these cancel out, so I’m left with x equals 4/3. What that tells me is it would take them 4/3 of an hour working together in order to mow this lawn. Before you start doing your start doing your homework problems, make sure you’re not doing the meatball answer. The meatball answer for this kind of problem would be well if Brooks mows it in 4 hours, Jeremy mows it in 2 hours, the meatball would say oh it takes them 6 hours working together. No it doesn’t 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 answer.
Unit
Word Problems Using Systems of Equations