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

because they could drop even lower..

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.