Question

I need help on number 14!!! Please help and justify your answer!! PLEASE

Answer 1

as the rate of company B is greater, the company B will reach the top first

Step-by-step explanation

to solve this we can find the rate of each company and then compare

let

`rate=\frac{finished\text{ length of construction}}{time\text{ taken}}`

so

Step 1

convert the mixed number into fractions

remember how

`a(b)/(c)=((a*c)+b)/(c)`

so

`\begin{gathered} 5\text{ }(1)/(2)=((5*2)+1)/(2)=(11)/(2) \\ 3\text{ }(1)/(2)=((3*2)+1)/(2)=(7)/(2) \end{gathered}`

Step 2

Find the rate of each company

A) Company A

replace

`\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_A=(550)/((11)/(2))=(1100)/(11)=100\text{ ft per month} \end{gathered}`

B) Company B

`\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_B=(385)/((7)/(2))=(770)/(7)=110\text{ ft per month} \end{gathered}`

Step 3

finally, compare

`\begin{gathered} 110\text{ ft per month }>100\text{ ft per month} \\ hence \\ rate_B>rate_A \end{gathered}`

as the rate of company B is greater, the company B will reach the top first