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Rational Function problems

I need some help instructing me how to complete the following questions:

Part 1: From a 220 feet high lighthouse in the Bahamas island of Nassau, a person sees a ship on the horizon. Due to the curvature of earth, how far is the ship from the lighthouse?

Use the formula: d = sqrt[3h/2], where d is the distance in nautical miles and h is the height in feet.
Provide a similar example of when you were close to the beach, or elsewhere. Estimate how high above sea level you are and find how far the ship is from you.

Part 2: An application of a rational function is T = (AB)/(A+B), which gives the time, T, it takes for two workers to complete a particular task where A & B represent the time it would take for each individual worker to complete the identical task working alone. It takes William 3 hours longer than Timothy to paint a 4x 5 feet bedroom. Respond to the following:

Working together, both can complete the job in 2 hours. How long does it take each one to complete the painting job working alone?

Solution Preview

Part 1.

d=sqrt(3h/2) = sqrt(3*220/2) = sqrt(330) = 18.17 nautical miles.

A similar example:

Suppose that you are standing on a tower which is 500 feet tall. You see a train on the horizon. How far is the train in KILOMETERS?

Using the formula, we get d = sqrt(3h/2) = sqrt(3*500/2) = sqrt(750) = 27.39 ...

Solution Summary

Rational Functions