Question

A welder requires 18 hours to do a job. After the welder and an apprentice work on a job for 6 hours, the welder moves to another job. The apprentice finishes the job in 14 hours. How long would it take the apprentice, working alone, to do the job?

Answer 1

Answer:

the apprentice can complete the job in 30 hours by working alone.

Step-by-step explanation:

Given:

Number of hours required to complete a job by welder = 18 hours

Number of hours welder work on job = 6 hours.

Number of hours required by apprentice to complete the job = 14 hours

We need to find Number of hours required to complete a job by apprentice alone.

Solution:

Let Number of hours required to complete a job by apprentice alone be 'a'.

Also let the job completed be = 1

Now we know that ;

Time required on job is equal to sum of Number of hours welder work on job and Number of hours required by apprentice to complete the job.

framing in equation form we get

Time required on job =  $6+14 =20\ hrs$

Now we can say that;

each has done a fraction of the work so we will add to two fraction as number of hours of work done by Total number of hours required to do the work to complete 1 job.

so we can frame the equation as;

$\frac{6}{18}+\frac{20}{a}=1$

By reducing the fraction we get;

$\frac{1}{3}+\frac{20}{a}=1$

Now we will make the denominator common to solve the fraction we get;

$\frac{1\times a}{3\times a}+\frac{20\times3}{a\times3}=1\\\\\frac{a}{3a}+\frac{60}{3a}=1$

Now denominators are same so we will solve the numerator we get;

$\frac{a+60}{3a}=1$

Multiplying both side by 3a we get;

$\frac{a+60}{3a}\times3a=1\times 3a\\\\a+60=3a$

Combining the like terms we get;

$3a-a=60\\\\2a=60$

Dividing both side by 2 we get;

$\frac{2a}{2}=\frac{60}{2}\\\\a=30\ hrs$

Hence the apprentice can complete the job in 30 hours by working alone.