Question

If Phumza and Nathi eat together, they can eat 480 hamburgers in 6 hours. However, eating alone, Nathi takes 16 hours longer than Phumza would eat 480 hamburgers.
How long does it take Phumza to eat 480 hamburgers?

Answer 1

Let's say phumba can eat $"x"$ hamburger while Nathi can eat $"y"$ hamburger

Time taken 6 hours

Therefore we can say together they can eat

$6(X+y)=480....(1)$

Phumba alone can eat for $"t"$ hours

$tx=480\\t=\frac{480}{t}$

Nathi alone can eat

$(t+16)y=480\\t=\frac{480}{t+16}$

Substitute values of X and y in equition 1

$6(\frac{480}{t}+\frac{480}{t+16}=480\\\frac{480}{t}+\frac{480}{t+16}=80\\\frac{480(t+16)+480t}{t(t+16)}=80$

$=480(t+16)+480t=80t(t+16)\\=6(t+16)+6t=y(t+16)\\=6t+96+6t=t^2+16t\\0=t^2+16t-12t-96\\0=t^2+4t-96\\t^2+4t-96=0$

$t^2+12t-8t-96 =0\\t(t+12)-8(t+12)=0\\(t+12)(t-8)=0\\t=-12,t=8$

t cannot be negative, therefore t=8

Phumba takes 8 hours to eat 480hamburgers