Sydney takes 3 hours longer that Toni to clean the garage. If they work together, it takes them 2
1 answer:
Answer:
6 hours
Step-by-step 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
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