Answer:
It would take the apprentice 14 hours to make the fireplace on his own.
Step-by-step explanation:
Let x represent the hours it takes the bricklayer to make a fireplace on his own and x + 10 represent the hours it takes the bricklayer's apprentice to make a fireplace on his own.
7/(x + 10) + 2/x = 1
<em>7/(x+10) represents the fraction of the fireplace the bricklayer's apprentice made (total amount of time the bricklayer's apprentice worked on the fireplace/time it takes the bricklayer's apprentice to make a fire place on his own) while 2/x represents the fraction of the fireplace the bricklayer made (total amount of time the bricklayer worked on the fireplace/time it takes the bricklayer to make a fire place on his own). The 1 on the right side of the equation represents the number of fireplaces they made in that time.</em>
<em>Multiply both sides of the equation by x(x + 10) to get rid of the denominators:</em>
x(x + 10)[7/(x + 10) + 2/x] = x(x + 10)1
x(x + 10)[7/(x + 10)] + x(x + 10)(2/x) = x(x + 10)
7x + 2(x + 10) = x² + 10x
7x + 2x + 20 = x² + 10x
<em>Gather all the terms to one side of the equation:</em>
x² + 10x - 7x - 2x - 20 = 0
x² + x - 20 = 0
<em>Factoring the simplified equation:</em>
(x + 5)(x - 4) = 0
<em>Solving for each factor:</em>
When x + 5 = 0,
x = -5
When x - 4 = 0,
x = 4
<em>Since a negative solution wouldn't make sense for this question, it would take the bricklayer 4 hours to complete the fireplace on his own.</em>
<em>Substituting x = 4 into x + 10 to find out how long it would take the apprentice to make the fireplace on his own:</em>
x + 10 = 4 + 10 = 14
Therefore, it would take the apprentice 14 hours to make the fireplace on his own.
