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Billy142

by Billy142 at July 08, 2011

You are racing a child that you are twice as fast as and you want to give him a head start in a race from one side of a field to the other. How much of a head start should you allow so that you will come close to finishing the race even? Draw a picture and label the length of the field as L and the head start distance as H. What is the length that the child needs to run? If your speed is S what is the child's speed? You want to finish at nearly equal times; the time that it takes you would be L/S (the distancerun divided by the speed run), what would it be for the child? Set those equal and solve for H.

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Billy -This is a tricky problem, but if you look closely at the words it will become very easyThe main question is to solve for H.  Well, here is the tricky part.  If you run twice as fast then the child needs to start at a distance equal to L/2.  Let's look at an example with numbers:Say the field is 1000 feet and you can run it in one minute.  The child can only run half as fast as you, right?  So the child runs at 500 feet/min.  Well, if you both want to finish the race in one minute, the child would have to start half way down the field or at the halfway  point.  In this example, that would be 500 feet down the field.So if your speed is S, then the child's speed is S/2.  If the field is length L, then the child must run L/2 in order for both to cross the finish line at the same time.Hope that helps
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Steve204 Steve204 July 08, 2011

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