Question 828314: It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own.
Found 2 solutions by ptaylor, josmiceli:
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! First, we want to determine the rate at which both John and Brian work.
Since we don't know how long it takes John to build the car, we will let x denote this time.
If it takes John x hours to build the car, then we know that it takes Brian (x+15) hours to build the car because that's what the problem states.
If we can set up an equation that determines x, then all we need to do is add 15 hours to it and we have Brian's time.
Now, we can determine the rate at which each boy works. We can clearly see that John works at the rate of 1/x of the model car per hour and Brian works at the rate of 1/(x+15) of the model car per hour.
We are told that if they work together, they can build the model car in 4 hours which means that, together, they work at the rate of 1/4 of the model car per hour.
We also know that, together, they work at the rate of 1/x + 1/(x+15) of the model car per hour.
Thus, our equation to solve is:
1/x + 1/(x+15)=1/4
When we solve this equation for x and add 15 hours to it, we will have solved the problem:)
Hope this helps---ptaylor
Answer by josmiceli(19441)  (Show Source):
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