Answer:
It will take him 12 hours working alone
Explanation:
In this question, we are asked to calculate the time in hours it will take a roofing contractor to finish a job alone given the amount of time he and his assistant will finish the roof job.
We can identify from the question that he works 2 times as fast as his assistant. So let’s say he takes x hours, his assistant will take 2x hours
Now, let’s say the span of the roofing work is y meters.
His rate will be y/x and his assistant will be y/2x while their joint rate will be y/8
Now if their individual rates are added together, we will have the joint rate
Mathematically;
y/x + y/2x= y/8
y(1/x + 1/2x) = y(1/8)
1/x + 1/2x = 1/8
3x/2x^2 = 1/8
3/2x = 1/8
2x = 24
x = 24/2
x = 12 hours