Question

The Fun Committee is hosting the Annual City Festival. Jennifer is in charge of the committee and is planning a race to raise money for the Festival. The runners will earn money from donors for the number of miles they run. If the runners start at the park, run to City hall, and then run back to the park, how many total miles will each runner run? Show your work and leave your answer in simplest radical form if necessary.

Answer 1

Answer:
`6√(5)` miles

This is the same as writing 6*sqrt(5) miles

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Work Shown:

P = park

C = city hall

Point P is at the location (10,11)

Point C is at the location (7,5)

Apply the distance formula to find the length of segment PC

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((10-7)^2 + (11-5)^2)\\\\d = √((3)^2 + (6)^2)\\\\d = √(9 + 36)\\\\d = √(45)\\\\d = √(9*5)\\\\d = √(9)*√(5)\\\\d = 3√(5)\\\\d \approx 6.7082039\\\\`

The exact distance between the park (P) and city hall (C) is
`3√(5)` miles.

This doubles to
`2*3√(5) = 6√(5)` miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.

Extra info:

`6√(5) \approx 13.41641` so the runner travels a total distance of roughly 13.4 miles.