Question

Sydney takes 3 hours longer that Toni to clean the garage. If they work together, it takes them 2

hours. How long would it take Sydney working alone to clean the garage?

Answer 1

6 hours

Explanation:

The formula for work is

1/a + 1/b = 1/c

where a and b are the times working alone and c is the time working together

Let x= time for Sydney

x-3 = time for Toni

1 /x + 1/ ( x-3) = 1/2

Multiply by 2x(x-3) to clear the denominators

2x(x-3)(1 /x + 1/ ( x-3)) = 1/2 *2x(x-3)

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

Distribute

2x-6 +2x = x^2 -3x

Combine like terms

4x-6 = x^2 -3x

Subtract 4x from each side

-6 = x^2 -3x-4x

Add 3 to each side

0 = x^2 -7x +6

Factor

0 = (x-6) (x-1)

Using the zero product property

x-6 = 0 x-1 =0

x=6 x=1

But x cannot =1 because that is less time than together

x=6