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Kevin and his little brother both start at the same level. The rate that the two brothers gain levels is constant. If Kevin gains levels $1.5$ times as fast as his brother, and at the end of two hours, Kevin is six levels higher than his brother, how many levels does Kevin gain per hour?

What I did :

So I start by making equations of things I know. So since Kevin is $1.5$ times faster than his brother I can make the equation $x = 1.5y$ where $x$ is the speed of Kevin and $y$ is the speed of his brother. I plug this into the $D=rt$ equation and I get :

$$D = rt$$

$$D + 6 = 1.5y \cdot 2 $$

$$D + 6 = 3y$$

$$D = 3y - 6$$

So the equation above is for Kevin so the next equation would be for his brother

$$D = rt$$

$$D = 2y$$

So now since I can isolate $D$ on both sides I can get the equation :

$$2y = 3y - 6$$ $$y = 6$$

Since Kevin is $1.5$ times as fast as his brother $$x = 1.5y$$

$$x = 1.5(6)$$

$$x = 9$$

So would the answer be $9$? I think it is wrong because the question said he was $6$ floors higher. If anyone could help that would be great.

bames
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Atrey Desai
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  • You are correct. After $2$ hours, at a rate of $9$ levels per hour, Kevin has gained $18$ levels. His brother, on the other hand, has gained only $2\cdot 6 = 12$ levels, which is $6$ fewer than Kevin. – bames Mar 05 '18 at 01:02
  • Oh thanks, I was confused because I didn't plug in 9 into D=rt so I thought 9-6= 3 which is wrong. – Atrey Desai Mar 06 '18 at 05:41

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