Three students have started a fence-painting business. Working together, Pragnesh and Qazi can paint the fence in 2 hours. Similarly, Pragnesh and Ronghui can paint the
fence in 3 hours when they work together. Finally, when Qazi and Ronghui work together, they can
paint the fence in 4 hours. How long would it take if all three students worked together to paint the

4 1/2 hours

Step-by-step explanation:

Pragnesh = 30 minutes

Qazi = 1 1/2 hours

Ronghui = 2 1/2 hours

add them and that gets you 4 1/2 hours. You can also check this yourself by putting this in the number problem. :)  

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.