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A long distance runner starts at the beginning of a trail and runs at a rate of 4 miles per hour. Three hours later, a cyclist starts at the beginning of the trail and travels at a rate of 19 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?


Do not do any rounding.

Verified Answer :

bartdrinksmalk

After \(h\) hours, the distance the runner went is
\(4h\)
and the distance the cyclist went is
\(19(h-3)\)

Set the two equations equal and solve for \(h\):
\(4h=19(h-3)\)
\(\Rightarrow 4h=19h-57\)
\(\Rightarrow -15h=-57\)
\(\Rightarrow h=\frac{57}{15}\)
\(\Rightarrow h=\frac{19}{5}\)
\(\Rightarrow h=3.8\)

The cyclist traveled \(h-3\) hours, which is 0.8 hours

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