Answer:
It would take them [tex]\frac{110}{21}[/tex] or approximately 5.24 hours together
Step-by-step explanation:
Use the algebra work formula, [tex]\frac{1}{tb}[/tex] = [tex]\frac{1}{t1}[/tex] + [tex]\frac{1}{t2}[/tex], where tb is the time together, t1 is the time of one person individually, and t2 is the time of the other person.
Plug in 10 and 11:
[tex]\frac{1}{tb}[/tex] = [tex]\frac{1}{t1}[/tex] + [tex]\frac{1}{t2}[/tex]
[tex]\frac{1}{tb}[/tex] = [tex]\frac{1}{10}[/tex] + [tex]\frac{1}{11}[/tex]
Find the common denominator, then add the fractions together:
[tex]\frac{1}{tb}[/tex] = [tex]\frac{11}{110}[/tex] + [tex]\frac{10}{110}[/tex]
[tex]\frac{1}{tb}[/tex] = [tex]\frac{21}{110}[/tex]
Cross multiply and solve for tb:
110 = 21tb
5.24 = tb
So, it would take them [tex]\frac{110}{21}[/tex] or approximately 5.24 hours together
