Algebra word problem

Question

A sawmill cuts boards for a lumber supplier. When he saws A, B, and C all work for 6 hr, they cut 7200 linear board-ft of lumber. It would take saws A and B working together 9.6 hour to cut 7200 ft of lumber. Saws B and C can cut 7200 ft of lumber in 9 hr. Find the rate (in ft/hr) that each saw can cut lumber. 

Answer 1

I am going to write the equations to solve this problem. In order to understand the solution you must figure out that the numbers which look like reciprocal are RATES!

(1/A) + (1/B) + (1/C) = 7200/6 = 1200 equation (1)

(1/A) + (1/B) = 7200/9.6 = 750 equation (2)

(1/B) + (1/C) = 7200/9 = 800 equation (3)

Subtract equation (2) from equation (1) to get 1/C = 450

Substitute the value of 1/C into equation (3) to get 1/B = 350

and use this value in equation (2) to get 1/A = 400

These numbers are the rates for A, B and C respectively. If you multiply 6 (400+350+450), you get 7200 as required.

If you have not seen work problems before, you will need to think through what I have told you to understand why this solution works.