From a 220 feet high lighthouse in the Bahamas island of Nassau, a person sees a

Question

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?
Provide a similar example, set up the equation and solve the problem.
Show you work step by step and explain your work step by step.

Explanation / Answer

d = SQRT[3h/2] = SQRT[3*220/2] = SQRT[330] = 18.2 miles You are riding piggyback on your brother who is wading in the water. Your eyes are six feet above sea level and you see a burning log at the horizon. How far away is it? (the height of the ship is also important, so I picked something low so as not to introduce much error.) d = SQRT[3*6/2] = SQRT[9] = 3 miles Part 2 Wil = Tim + 3 A = Wil B = Tim T = 2 hours 2 = (3+Tim)(Tim)/[(3+Tim)+(Tim)] multiply both sides by the denominator 2*[(3+Tim)+(Tim)] = (3+Tim)(Tim)/[(3+Tim)+(Tim)]*[(3+Tim)+(Tim)] distribute 6 + 4Tim = 3Tim + Tim^2 Tim^2 - Tim - 6 = 0 Factor (Tim +2)(Tim -3) = 0 Tim = -2 hours or 3 hours 3 hours makes sense. -2 hours is not possible (Math sometimes gives non-physical answers) Timothy alone takes 3 hours William alone takes 6 hours Let's check this in one hour Timothy does 1/3 of the job In one hour William does 1/6 of the job So, in two hours Timothy does 2/3 and William does 2/6 2/3 + 2/6 = 2/3 + 1/3 = 1, or 100% of the job. Yes, this checks. Jim can do a job in two hours. Pam can do a job in three hours. How long will it take them if they work together? T = 2*3/(2+3) = 6/5 hours = 1 hour and ten minutes {since 1/5*60 = 10}

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