Two teams working together can finish a job in 8 days. if the first team works alone for two days and the second team works alone for 5 days, 5/8 of the total work still remains. How many days will it take each team to finish the work alone?

x is the days that the first team finishes the work alone (x>8)

y --------------------------second-----------------------------------------(y>8)

In a day:

⇒          [tex]\frac{1}{x}+ \frac{1}{y} =\frac{1}{8}[/tex]               (1)

If the first team works alone for two days and the second team works alone for 5 days, 5/8 of the total work still remains:

⇒          [tex]\frac{2}{x}+\frac{5}{y}=\frac{3}{8}[/tex]                (2)

(1),(2)   ⇒   [tex]\left \{ {{\frac{1}{x}+ \frac{1}{y} =\frac{1}{8}} \atop {\frac{2}{x}+\frac{5}{y}=\frac{3}{8}}} \right. <=>\left \{ {{x=16} \atop {y=24}} \right.[/tex]

It'll take the first team 16 days and the second team 24 days to finish the work alone

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