Answer: t = 6.67 hours
Step-by-step explanation:
From the information given,
Diego can lay a slab of concrete in 15 hours. This means the rate at which he can lay the slab = 1/15
Luis can do it in 12 hours. The rate at which he lay the slab = 1/12
Let t represent the number of hours it will take them to work together. It means that the rate at which they can lay the slab together is 1/t
Since the rates are independent of each other, then
1/15 + 1/12 = 1/t
The lowest common multiple of the denominator is = 60
Thus,
(4 + 5)/60 = 1/t
9/60 = 1/t
By taking reciprocal of both sides,
t = 60/9
t = 6.67
It will take 6.67 hours for them to work together