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

`(4)/(5)` hour

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:

`(1(3)/(10))/(x)=(3(1)/(4))/(2)`

`((13)/(10))/(x)=((13)/(4))/(2)`

`(13)/(10\cdot x)=(13)/(4\cdot 2)`

Cross multiply:

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

`10\cdot x=4\cdot 2`

`(10\cdot x)/(10)=(4\cdot 2)/(10)`

Therefore, it will take
`(4)/(5)` hour to complete
`1(3)/(10)` mile state fair​ race.