Q1 Assume that all workers work at the same constant pace It

Q1: Assume that all workers work at the same constant pace. It takes three workers 4 hours lay the brick for a 50 square foot raised rectangular patio. The owner decides to scale the planar dimensions of the patio by a factor of three (the height remains unchanged) and hires instead six workers. How many hours will it take to complete the project?

Note to answerer: Could you briefly explain the steps and reasonings behind solving this problem, also? Thank you!

Solution

let the amount of work be w

number of workers =3, work hours =4

amount of work done by a worker in an hour =w_/(3*4)

amount of work done by a worker in an hour =w_/12

when 6 six workers are hired

amount of work done by 6 workers in an hour =6w_/12

amount of work done by 6 workers in an hour =w_/2

amount of time required for 6 workers to complete work w is =w_/(w/2) =2 hours

The owner decides to scale the planar dimensions of the patio by a factor of three =>length oncreases by factor of 3 , width increases by factor of3 . so area increases by a factor of 3²=9

=> work in increased by 9 times

so amount of time required for 6 workers to complete work 9w is = 9*2=18 hours

it will take 18hours to complete the project