*machine x can produce 1,200 bolts in 4 hours and machine y can produce 1,000 bolts in 5 hours. working together at these constant rates, how long will it take it them to produce 1,000 bolts

This is the concept of proportionality.To solve the expression we proceed as follows;
Machine X;
Proportion of work completed in 1 hour will be:
1/1200

Machine Y;
Proportion of work completed in 1 hour will be:

1/1000

Proportion of work completed by both machines in 1 hour will be:
1/2000+1/1000
=3/2000
number of bolts produced by both machines in 1 hour will be:
666 2/3 bolts;
Time taken to produce 1000 bolts will be:
1000/[666 2/3]
=1 1/2 hours

Step 1: 6x-10=1; step 2: 6x=11