Bob can type 2 letters in 4 hours while bill can do it in 6. how many hours would it take them, working together, to type six letters?

5 1/7 hours

Step-by-step explanation:

We're looking to calculate TIME.  In this situation the proper expression is:

              6 letters

time =

            2 letters / 4 hours  +  2 letters / 6 hours

We can divide numerator and denominator both by "2 letters" to simplify the problem:

                     3                          3 hours             3 hours

time = hours, or =

              1/4  + 1/3                     3/12 + 4/12           7/12

Invert the divisor 7/12, and then multiply:  (3 hours) (12/7) = 36/7 hours, or

5 1/7 hours

It will take these two guys 5 1/7 hours, working together, to type these 6 letters.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240