Question

An engineer said be could finish a highway section in $3$ days with his present supply of a certain type of machine. However, with $3$ more of these machines the job could be done in $2$ days. If the machines all work at the same rate, how many days would it take to do the job with one machine?

• A. $6$
• B. $12$
• C. $15$
• D. $18$
• E. $36$

Answer 1

The correct option is D $18$

suppose that the work done by each machine is $X$

and the total number of machine initially=$Y$

now, according to the quetion we have

$3XY=1$........(1)

$2(XY+3Y)=1$.........(2)

so from (1) and (2) we get

$2$($\frac{1}{3}$+$3X$)=$1$

$\frac{1}{3}$+$3X$=$\frac{1}{2}$

$3X$=$\frac{1}{2}$-$\frac{1}{3}$

$3X$=$\frac{1}{6}$

$X$=$\frac{1}{18}$

so that the single machine will take $18$ days to complete the work.

so option $D$ is correct.