唔識做功課63

Let the time Andy requires to lay the tiles alone be x hours, the time Lawrence requires to lay the tiles alone be y hours. Then,

y = x - 5/3 - (1)
It is known that Andy and Lawrence can do 1/x and 1/y of work in 1 hour respectively. Therefore,
(total proportion of work that Andy and Lawrence can do together in 1 hour)×(number of hours required) = 1 <--- (that means the whole work)
=> (1/x + 1/y)×2 = 1
=> 2y + 2x = xy - (2)
Sub. (1) into (2),
2(x - 5/3) + 2x = x(x-5/3)
2x - 10/3 + 2x = x² - 5x/3
3x² - 17x + 10 = 0
(3x - 2)(x - 5) = 0
x = 2/3 or x = 5
when x = 2/3, y = 2/3 - 5/3 = -1 (rej. since no. of hours cannot be -ve)
when x = 5, y = 10/3.
∴ Andy requires 5 hours to lay the tiles alone.