Master and his assistant working together can finish building a room in 15 days. How long would it take each of them to build the room working separately, if it is known that the master can finish it 16 days earlier than the assistant?

The master takes 24 days and the assistant takes 40 days.

Step-by-step explanation:

Let y be the number of days the master takes to build the room and x the number of days the assistant takes.

Ten, working the fraction of the room they can individually build in a day:

1/ x + 1/y = 1/15.

Also  y = x - 16

Substituting for y in the first equation:

1/x + 1/ (x - 16) = 1/15

Multiply through by the LCD  15x(x - 16):

15(x - 16) + 15x =  x(x - 16)

15x + 15x - 240 = x^2 - 16x

x^2 - 16x - 30x + 240 = 0

x^2 - 46x + 240 = 0

(x  - 40)(x - 6) = 0

x = 6, 40.

Now , as y = x - 16 x must be 40, and y =  40 - 16 = 24 days.

So the assistant takes 40 days to build the room and the master takes  24 days.

5104.38 inches

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.