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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?

Respuesta :

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

[tex]3*40=120mi[/tex]

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:

[tex]\begin{gathered} d=40t+120 \\ d=50t \end{gathered}[/tex]

equating both expressions and solving for t, we get:

[tex]\begin{gathered} 40t+120=50t \\ \Rightarrow50t-40t=120 \\ \Rightarrow10t=120 \\ \Rightarrow t=\frac{120}{10}=12 \\ t=12 \end{gathered}[/tex]

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

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