### Math Notes

Subjects

#### Algebra Solutions

##### Topics || Problems

In what time would A, B and C together do a piece of work if A alone could do it in 6 hrs. more , B alone in 1 hr more, and C alone in twice the time?
Solution:

Let t be the total time A, B and C can do a piece of work

Thus, A can do that work in t + 6, B in t +1, and C in 2t

Working together: $$\frac{1}{T} = \frac{1}{T+6} + \frac{1}{T+1} + \frac{1}{2T}$$

$$\frac {(t + 6)(t + 1)(2t)}{x} = (x+1)(2t) + (x+6)(2t) +(x+6)(c+1)$$

$$2x^2 +14x +12 =5x^2 +21x + 6$$

$$3x^2 +7x -6 = 0$$

$$(3x-2)(x+3) = 0$$

$$x = 2/3$$ hours

$$x = 2/3 (60)$$ = 40 minutes