How to do it in your head:
The LCM of 7 and 3 is 21. If they worked together for 21 hours,
Sam would finish 3 projects while Peter would finish 7 projects.
So in 21 hours they would finish 10 projects. So together they
could finish just 1 project in just 1/10th of that 21 hours or
2.1 hours, or 2 hours, 6 minutes.
How to do it with algebra:
Let x be the answer.
Make this chart
Projects No. of hours rate in
finished required projects/hour
Sam alone
Peter alone
Both together
We put the hours required in each case and 1 for the number of
projects completed, which is 1 in all three cases.
Projects No. of hours rate in
finished required projects/hour
Sam alone 1 7
Peter alone 1 3
Both together 1 x
Fill in the rates by dividing projects finished by hours:
Projects No. of hours rate in
finished required projects/hour
Sam alone 1 7 1/7
Peter alone 1 3 1/3
Both together 1 x 1/x
The equation comes from
+ 
= 
+ 
= 
Multilply through by LCD = 21x
3x + 7x = 21
10x = 21
x = 2.1 hours, or 2 hours 6 minutes
Edwin
