Mathematical Problem Solving: Distance And Work Rate Applications

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Mathematical Problem Solving: Distance and Work Rate ApplicationsSimilartyscore must be below 30%-so thework needs to be original, not copied off theinternet or payment will not be released.Part 1:My lighthouse is 220 feet tall. I have d = sqrt[3*220/2]= sqrt[330] = 18.17 nautical miles (thisvalue has been foundby using a calculator)If Iam close to the beach, let say at d = 10 nautical miles, I am at h above sea level. h isdetermined by the following equation :h = 2d²/3 = 2*100/3 = 66.7 feet high. That isalsohow far away the ship is from me.Part 2:1.Workingtogether, both can complete the job in 2 hours. How long does it take each oneto complete the painting job working alone?We have T= 2 hours = AB/(A+B) and B = A + 3 (if we assume A is Timothy time and B isWilliam time)Then : 2 = (A + 3)A/(A + A + 3) = A(A+3)/(2A + 3) = (A² + 3A)/(2A + 3)then : A² + 3A = 4A + 6 then A²-A6 = 0We solve this equation by factoring : A²-A-6 = (A-3)(A+2) = 0then the solutions for A are A = 3 and A =-2 (negative result which is impossible for a timevalue)Therefore the only possible solution is A = 3 hours and then B = 3+3= 6 hoursWe can choose another example by varying the Timothy time to paint a 4x5 feet bedroom : let A= 7 hours. Then B = A + 3 = 7+3 = 10 hours.Therefore T = AB/(A+B) = (7*10)/(7+10) = 70/17 = 4.12 = 4.1 hours to complete this task bythe two workers working together.

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