# Chapter 2 - Solving Equations - 2-7 Solving Proportions - Practice and Problem-Solving Exercises - Page 128: 38

Approximately 5 meters

#### Work Step by Step

$Step 1)$ We have the information to the left from the problem. By looking at this information as well as the question being posed in the problem, we can deduce that the race will take 13.4 seconds to complete. We know this because Maya has to run the entire race (Amy is getting a head start) and it takes Maya 13.4 seconds to run that distance (100m). $Step 2)$ We can begin setting up our proportion by noting just Amy's facts. $Step 3)$ (100/14.1) = (x/13.4) ... This is the proportion that will solve the DISTANCE Amy is able to travel in 13.4 seconds. We are specifically looking for this distance because that is all the time Amy is going to have to run $Step 4)$ We begin solving for x by cross multiplying. $Step 5)$ Then continue by simplifying both sides of the equation. Our next step will by to divide both sides of the equation by 14.1. $Step 6)$ x is approximately equal to 95. This indicates that Amy can run approximately 95 meters in 13.4 seconds. Due to this, we can deduce that she will need a 5 meter head start (100 meters - 95 meters) over Maya in order to finish the race at the same time. $Step 7)$ So the final answer is approximately 5 meters.

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