Answer:
[tex]3\frac{1}{3}[/tex] or [tex]\frac{10}{3}[/tex]
Step-by-step explanation:
We could use the combined rate equation to find the combined rate of work.
Combined rate of work formula: [tex]\frac{1}{t_{b}} = \frac{1}{t_{1} } + \frac{1}{t_{2} }[/tex], where [tex]t_{1}[/tex] is the individual time for object A, [tex]t_{2}[/tex] the individual time for object B and [tex]t_{b}[/tex] is the time for A and B together.
The time it takes Irina to paint the room alone, [tex]t_{1}[/tex] = 5 hours
The time it takes Paulo to paint the room, [tex]t_{2}[/tex] = 10 hours
1) Substitute object A (Irina) and B (Paulo) into the formula given above, and change [tex]t_{b}[/tex] into an [tex]x[/tex].
[tex]\frac{1}{{x}} = \frac{1}{5 } + \frac{1}{10 }[/tex]
2) Add the fractions.
[tex]\frac{1}{x} = \frac{3}{10}[/tex]
3) Solve for the [tex]x[/tex].
[tex]x(3) = 1(10)\\3x = 10\\x = \frac{10}{3} \\[/tex]
4) Change them into a mixed fraction.
[tex]3\frac{1}{3}[/tex]
Note: [tex]\frac{10}{3}[/tex] or [tex]3\frac{1}{3}[/tex] are both correct. Write the answer according to the question. In this case, there is no specific rule, so I choose [tex]3\frac{1}{3}[/tex].
