Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.1 Junior Find the answer

Qiang drives $15$ miles at an average speed of $30$ miles per hour. How many additional miles will he have to drive at $55$ miles per hour to average $50$ miles per hour for the entire trip?

Pick one

Solution

The only option that is easily divisible by $55$ is $110$ , which gives 2 hours of travel. And, the formula is $\frac{15}{30} + \frac{110}{55} = \frac{5}{2}$ .
And, $\text{Average Speed}$ = $\frac{\text{Total Distance}}{\text{Total Time}}$ .
Thus, $\frac{125}{50} = \frac{5}{2}$ .
Both are equal and thus our answer is $\boxed{\textbf{(D)}\ 110}.$

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