Question

The Smiths are moving across the country. Mr. Smith leaves 3 hours before Mrs. Smith. If he averages 40mph and she averages 50mph, how many hours will it take Mrs. Smith to catch up to Mr. Smith?

Answer 1

Since Mr Smith leaves 3 hours before Mrs Smith and he averages 40mph, the total distance that he covered in those 3 hours is:

`3*40=120mi`

let t be the time wher Mrs Smith catches up with Mr Smith, and let d be the distance between them. Then, we can write the following equations:

`\begin{gathered} d=40t+120 \\ d=50t \end{gathered}`

equating both expressions and solving for t, we get:

`\begin{gathered} 40t+120=50t \\ \Rightarrow50t-40t=120 \\ \Rightarrow10t=120 \\ \Rightarrow t=(120)/(10)=12 \\ t=12 \end{gathered}`

therefore, it will take Mrs Smith 12 hours to catch up to Mr Smith