Answer
Irene: 3h
Henry: 4.5h
Work Step by Step
It takes Irene x hours to finish work
It takes Henry x+1.5h (x+$\frac{3}{2}$h) to finish work
It takes them 1h 48minutes (1h +$\frac{4}{5}$h) to finish work together
Fractions of work they do in an hour:
Irene: $\frac{1}{x}$
Henry: $\frac{1}{x+\frac{3}{2}}$
Together: $\frac{1}{1+\frac{4}{5}}$
Equation:
$\frac{1}{1+\frac{4}{5}}$= $\frac{1}{x}$+$\frac{1}{x+\frac{3}{2}}$
$\frac{5}{9}$= $\frac{1}{x}$+$\frac{2}{2x+3}$
multiply by 9x(2x+3)
5x(2x+3)=9(2x+3)+18x
10$x^{2}$+15x=18x+27+18x
10$x^{2}$-21x-27=0
Quadtratic formula:
441-4$\times$10$\times$(-27)=1521
x=$\frac{21+or-\sqrt1521}{20}$
Time must be positive so the only answer is
x=3
