Question 1206862
<br>
If this problem is on a competitive timed test, then you can use the standard shortcut for solving problems like this involving two workers: If the times for the two workers to perform the job individually are A and B, then the time required for them to do the job together is {{{(A*B)/(A+B)}}}<br>
For this problem: {{{(14*8)/(14+8)=112/22=56/11}}}<br>
ANSWER: 56/11 hours, or 5 1/11 hours<br>
If this problem is on a test in a classroom where you are supposed to show a formal algebraic solution, then the solution might look something like this.<br>
Let x be the number of hours it takes the two of them together to do the job.<br>
1/8 = fraction of job the first belt does in 1 minute
1/14 = fraction of job the second belt does in 1 minute
1/x = fraction of job the two belts together do in 1 minute<br>
The fraction of the job they do together is the sum of the fractions of the job each does alone in 1 minute:<br>
{{{1/8+1/14=1/x}}}<br>
Multiply the equation by the least common multiple of the denominators, which is 56x:<br>
{{{7x+4x=56}}}
{{{11x=56}}}
{{{x=56/11}}}<br>
And here is a different formal method for solving the problem and any similar problem.<br>
8 times 14 is 112.<br>
In 112 minutes, the first belt could do the job 112/8 = 14 times; in 112 minutes the second belt could do the job 112/14 = 8 times.  So together in 112 minutes the two could do the job 14+8 = 22 times.<br>
And so the number of minutes it will take the two belts together to do the one job is 112/22 = 56/11 = 5 1/11.<br>