Question

Kim and Dominic can paint their apartment in $2$ days. Working alone, Kim can complete the job in $3$ days less than Dominic, working alone. How long would it take Kim to complete the painting, working alone?

• A. $3$ days
• B. $5$ days
• C. $4$ days
• D. None of these

Answer 1

The correct option is A $3$ days

Solution:

Let Kim can complete the work alone in $x$ days.

and Dominic can complete the work alone in $x+3$ days.

Let the completed job $=1$

A typical shared work equation;

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

or, $2(x+3)+2x=x(x+3)$

or, $x^2-x-6=0$

or, $(x-3)(x+2)=0$

or, $x=3$ or $x=-2$

$\therefore$ Kim can complete the work alone in $3$ days.

Hence, A is the correct option.