If Mary can finish the job in x hours alone, how many hours will it take Carol to do the same job alone?

Step-by-step explanation:

Let the total work be x or you can take it as 1 since it won't matter

Let the time taken by Mary to finish the work alone be y.

So the rate at which Mary finishes the work alone is x/y . Here we are taking the rate because for both Mary and Carol the rate at which they are doing work will always remain constant.

Now we also know that Carol works twice as fast as Mary so Carol's rate of work is 2*(x/y). Here * means multiplication symbol.

So there total rate of work when working together is 2*(x/y) + ( x/y). This is equal to 3*(x/y). Call this equation 1.

And we know from the question that when they work together, they can finish the work in 4 hours. So the rate at which both of them work together is x/4. Call this equation 2

Ok so now we know that their combined rate of work is 3*(x/y) as from equation 1 and x/4 as from equation 2. Putting them together:-

3*(x/y) = x/4

Here we can cut off x on both sides as both are on the numerator side:-

3/y= 1/4

This means y=12

So Mary will take 12 hours to complete the work and Carol will take 6 hours to complete the work if they work alone.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841