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 Question from Christie: Sam and Claudia start at the same time on a bike hike of 150 miles. Sam travels 3 miles per hour faster than Claudia and finishes the trip 8 1/3 hours before Claudia. At what rate in miles per hour does Sam travel?

Hi Christie,

I am going to use the fact that rate is distance over time, in your case miles over hours.

Suppose Claudia rides at a rate of $x$ miles per hour then, since Sam rides at 3 miles per hour faster that Claudia, Sam rides at $x + 3$ miles per hour.

Suppose Sam takes $t$ hours to ride the 150 miles then, since Claudia takes 8 1/3 longer than Sam, Claudia rides the 150 miles in $t + 8 1/3$ hours.

Now use $\mbox{rate} = \large \frac{\mbox{distance}}{\mbox{time}}.$

For Sam this gives

$x+3 = \frac{150}{t}.$

What is the equation for Claudia?

Solve the equations for $x.$

Penny

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