Question

A dog won a race at the local fair by running 3 and one fourth miles in exactly 2 hours. At this constant​ rate, how long does it take the same dog to run the 1 and three tenths ​-mile state fair​ race? Use ratio reasoning to solve.

Answer 1

Answer:

$\frac{4}{5}$ hour

Step-by-step explanation:

Let x represent time taken by dog to run the 1 and three tenths ​-mile state fair​ race.

We have been given that a dog won a race at the local fair by running 3 and one fourth miles in exactly 2 hours.

We will use proportions to solve our given problem as:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

We will equate both speeds as:

$\frac{1\frac{3}{10}}{x}=\frac{3\frac{1}{4}}{2}$

$\frac{\frac{13}{10}}{x}=\frac{\frac{13}{4}}{2}$

$\frac{13}{10\cdot x}=\frac{13}{4\cdot 2}$

Cross multiply:

$13\cdot 10\cdot x=13\cdot 4\cdot 2$

$10\cdot x=4\cdot 2$

$\frac{10\cdot x}{10}=\frac{4\cdot 2}{10}$

Therefore, it will take $\frac{4}{5}$ hour to complete $1\frac{3}{10}$ mile state fair​ race.