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Chapter 2: Problem 10

Two cars, a Toyota Yaris and a Jeep, are traveling in the same direction, although the Yaris is \(186 \mathrm{m}\) behind the Jeep. The speed of the Yaris is \(24.4 \mathrm{m} / \mathrm{s}\) and the speed of the Jeep is $18.6 \mathrm{m} / \mathrm{s}$. How much time does it take for the Yaris to catch the Jeep? [Hint: What must be true about the displacement of the two cars when they meet?]

Short Answer

Expert verified
Answer: It takes 32 seconds for the Toyota Yaris to catch up to the Jeep.

Step by step solution

01

Identify the distance each car travels

We need to find how far each car travels in the time it takes for the Yaris to catch up to the Jeep. We are given the speeds of each car. Let's denote the distance traveled by the Yaris as \(D_Y\), the distance traveled by the Jeep as \(D_J\), the speed of the Yaris as \(V_Y\) and the speed of the Jeep as \(V_J\). Then, we have, \(D_Y = 24.4t\) \(D_J = 18.6t\)
02

Find the equation to describe when the Yaris catches up to the Jeep

When the Yaris catches up to the Jeep, the difference in their distances traveled will be equal to the initial distance between them, which is 186 meters. Therefore, we have \(D_Y - D_J = 186\) Substituting the expressions for \(D_Y\) and \(D_J\) from Step 1, we get, \(24.4t - 18.6t = 186\)
03

Solve the equation for time (t)

Now let's solve the equation from Step 2 to find the time it takes for the Yaris to catch up to the Jeep: \(24.4t - 18.6t = 186\) \(5.8t = 186\) Now, divide both sides by 5.8: \(t=\frac{186}{5.8}=32\) So, it takes 32 seconds for the Toyota Yaris to catch up to the Jeep.

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