# Inverse Proportion: If 6 workers can perform a job in 12 hours, then...

#### KWF

##### Junior Member
Have I solved the following correctly?

If 6 workers can perform a job in 12 hours, 3 workers working at the same rate can perform the same work in how many hours?

Solution:

x = k/y

x = 6 workers; k = constant; y = 12 hours

6 workers = k/12 hours

k = 72 worker-hours

a = k/b

a = 3 workers; k = constant from above solution; b = unknown hours

3 workers = 72 worker-hours/b

b * 3 workers = 72 worker-hours

b = 72 worker-hours/3 workers = 24 hours

#### Subhotosh Khan

##### Super Moderator
Staff member
Have I solved the following correctly?

If 6 workers can perform a job in 12 hours, 3 workers working at the same rate can perform the same work in how many hours?

Solution:

x = k/y

x = 6 workers; k = constant; y = 12 hours

6 workers = k/12 hours

k = 72 worker-hours

a = k/b

a = 3 workers; k = constant from above solution; b = unknown hours

3 workers = 72 worker-hours/b

b * 3 workers = 72 worker-hours

b = 72 worker-hours/3 workers = 24 hours
CORRECT - however a bit long-winded!