Two machines pack identical kits at constant rates. Machine A would pack 240 kits by itself in $x$

Question

Two machines pack identical kits at constant rates. Machine A would pack 240 kits by itself in $x$ hours. Machine B would pack the same 240 kits by itself in $(x-6)$ hours, where $x>6$. When both machines work together without interfering with each other, they pack 240 kits in 4 hours. Write expressions, in terms of $x$, for the packing rates of A and B, in kits per hour.[2] Form an equation using their combined rate and show that it simplifies to $x^2-14x+24=0$.[3] Solve this quadratic equation, giving both roots.[2] State the number of hours A would take alone, explaining why the other root is inadmissible.[1]

Accepted Answer

(a) $\dfrac{240}{x},\dfrac{240}{x-6}$ kits/h. (b) $x^2-14x+24=0$. (c) $12,2$. (d)12 hours; reject 2 since $x>6$.

A combined production-rate model

A combined production-rate model

Solution:

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