1. Let x = number of holes I can dig per hour

2. Let y = number of holes my brother can dig per hour

3. Number of holes I can dig in eight hours: 8x = 1

4. Number of holes my brother and I can dig in 5 hours: 5x+5y=1

5. Therefore: 8x = 5x+5y

6. 3x = 5y

7. y =

8. x =                        (since 8x = 1)

9. Therefore, y =           In other words, in 40 hours, my brother can dig three holes.

10. Therefore, my brother can dig a hole in  hours, i.e. in 13 hours

11. This answer makes sense, because in 5 hours I can make  of a hole, and my brother can make  of a whole (i.e.  of a hole). The total is 1 hole, as expected.