Answer:
Step-by-step explanation:
Given
Mary requires [tex]16[/tex] minutes more than Antoine
If Antoine requires [tex]t[/tex] minutes
so time required by Mary is [tex]16+t[/tex]
in 1 one minute Antoine do [tex]\frac{1}{t}[/tex] minute
Mary does [tex]\frac{1}{16+t}[/tex]
Total work done in 6 minutes
[tex]\frac{6}{t}+\frac{6}{16+t}=1[/tex]
[tex]\frac{t+16+t}{(16+t)t}=\frac{1}{6}[/tex]
[tex]12t+96=t^2+16t[/tex]
[tex]t^2+4t-96=0[/tex]
[tex](t+12)(t-8)=0[/tex]
thus [tex]t=8 min[/tex]
Antoine requires 8 minute to complete the work by himself
