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If a marathon runner averages\({\bf{9}}.{\bf{5}}{\rm{ }}{{{\rm{mi}}} \mathord{\left/ {\vphantom {{{\rm{mi}}} {\rm{h}}}} \right. \\} {\rm{h}}}\), how long does it take him or her to run a\(26.22{\rm{ mi}}\)marathon?

Short Answer

Expert verified

Time required by him or her to cover \(26.22{\rm{ mi}}\) will be \(2.76{\rm{ h}}\).

Step by step solution

01

Given data

Consider the given data as below.

Average speed,\(v = 9.5{\rm{ }}{{{\rm{mi}}} \mathord{\left/ {\vphantom {{{\rm{mi}}} {\rm{h}}}} \right. \\} {\rm{h}}}\)

Distance, \(d = 26.22{\rm{ mi}}\)

02

Required formula:

If you know how far something has traveled and how long it took to get there,

you can calculate its average speed.

Thespeedatwhichanobject'slocationchangesinanydirection.

The distance traveled in relation to the time it took to travel that distance is

how speed is defined.

\(v = \frac{d}{t}\) ….. (1)

Here,\(v\)is the velocity,\(d\)is the distance, and\(t\)is time.

03

Determine the time:

The time takes for him or her to run amarathon is define by rearranging equation (1).

\(t = \frac{d}{v}\)

Substitute \(9.5{\rm{ }}{{{\rm{mi}}} \mathord{\left/ {\vphantom {{{\rm{mi}}} {\rm{h}}}} \right.} {\rm{h}}}\) for \(v\) and \(26.22{\rm{ mi}}\) for \(d\) in the above equation.

\(\begin{array}{c}t = \frac{{26.22{\rm{ mi}}}}{{9.5{\rm{ }}{{{\rm{mi}}} \mathord{\left/ {\vphantom {{{\rm{mi}}} {\rm{h}}}} \right.} {\rm{h}}}}}\\ = 2.76{\rm{ h}}\end{array}\)

04

Conclusion:

Time required by him or her to cover \(26.22{\rm{ mi}}\) will be \(2.76{\rm{ h}}\).

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