Question 593760: Brian and Jake left their homes, which are 500 miles apart, and drove straight toward each other. It took 4 hours for the two to meet. If Jakes speed was 15 MPH slower than Brian's speed, what was Brian's speed?
Can you please solve this and explain to me how it's done? I am very confused about word problems and am not very good at them! Thanks for the help!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! This problem is based on the fact that the Distance traveled is equal to the Rate (or Speed) multiplied by the Time.
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In equation form this is written as:
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D = R*T
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You are probably already familiar with this equation. Think: if you travel at a rate of 60 miles per hour for 2 hours, the distance you go is 60 times 2 and this equals 120 miles. Pretty straightforward.
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In this problem, the rates for Brian and Jake are both unknown. What do you know from the problem? For one thing, you know that they are 500 miles apart. So the combined distance that they travel to meet has to equal 500 miles. You also know that they each drive 4 hours.
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Let's call Brian's rate B and let's call Jake's rate J. The distance that Brian drives is equal to his rate (B) times the time that he drives (4 hours). Similarly, the distance that Jake travels is equal to his rate (J) times the time that he drives (also 4 hours). Since the sum of these two distances is 500 miles, we can write the equation for adding the two distances as:
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B*4 + J*4 = 500
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The problem also tells us that Jake's speed is 15 mph slower than Brian's speed. Therefore, if we add 15 mph to Jake's speed (J) it would be equal to Brian's speed (B). So we can write this as:
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J + 15 = B
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and by subtracting 15 from both sides of this equation we then know that Jake's speed is equal to:
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J = B - 15
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That being the case we can return to the equation for the sum of the Distances:
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B*4 + J*4 = 500
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and for J in that equation we can substitute its equal of B - 15. This converts the distance equation to:
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B*4 + (B - 15)*4 = 500
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We then do the distributed multiplication by multiplying 4 times each of the terms in the parentheses to get:
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B*4 + B*4 - 60 = 500
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Combine the two terms involving B to get
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B*8 - 60 = 500
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Add 60 to each side to reduce this equation to:
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B*8 = 560
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and finally, solve for Brian's speed by dividing both sides of this equation by 8 to get:
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B = 70
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Brian's speed was 70 mph and Jake's speed (15 mph slower than 70 or 55 mph). The distance traveled by each is then:
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Brian at 70 mph for 4 hours = 280 miles. And Jake at 55 mph for 4 hours is 220 miles. The combined distance is 280 miles plus 220 miles and this sum covers the 500 miles originally between them. So the answer checks out.
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Hope this helps you to see how to work this problem.
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