Question

mia, sam, and ben are cross - country teammates running a practice loop known as \the mix,\ which covers 5 miles of varying terrain. their coach recorded the time it took each runner to complete their first serious segment of the loop.

• mia ran \\(\frac{3}{4}\\) of a mile in \\(\frac{1}{6}\\) of an hour.
• sam ran \\(\frac{5}{6}\\) of a mile in \\(\frac{2}{9}\\) of an hour.
• ben ran \\(1\frac{1}{2}\\) miles in \\(\frac{3}{5}\\) of an hour.

1. if mia, sam, and ben all run the course at a constant pace, which runner covered the greatest distance in the first full hour of running?

Explanation:

Step1: Find Mia's speed

Speed = Distance / Time. Mia's distance is $\frac{3}{4}$ mile, time is $\frac{1}{6}$ hour. So speed $v_{Mia}=\frac{\frac{3}{4}}{\frac{1}{6}}=\frac{3}{4}\times6 = \frac{18}{4}=4.5$ miles per hour.

Step2: Find Sam's speed

Sam's distance is $\frac{5}{6}$ mile, time is $\frac{2}{9}$ hour. Speed $v_{Sam}=\frac{\frac{5}{6}}{\frac{2}{9}}=\frac{5}{6}\times\frac{9}{2}=\frac{45}{12} = 3.75$ miles per hour.

Step3: Find Ben's speed

Ben's distance is $1\frac{1}{2}=\frac{3}{2}$ miles, time is $\frac{3}{5}$ hour. Speed $v_{Ben}=\frac{\frac{3}{2}}{\frac{3}{5}}=\frac{3}{2}\times\frac{5}{3}=\frac{5}{2}=2.5$ miles per hour.

Step4: Compare speeds

Compare 4.5, 3.75, and 2.5. 4.5 is the largest (Mia's speed).

Answer:

Mia