A roofing contractor can shingle a roof in half the time it takes his assistant. Working together, they can shingle the roof in 8 hours. How much time does it take the roofing contractor to finish the job alone

It will take him 12 hours working alone

Step-by-step 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

the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)