Answer to Question #256515 in Algebra for Andrew

Question

All outbound packages from a distribution center are routed to a person for packing. 60% of packages are easy and can be packed at a rate of 45 packages per hour. The remaining packages are more difficult and can only be packed at a rate of 12 packages per hour. There is no specialization, packages are randomly assigned to any available packer. What is the average packing rate for each packer?

Answer 1

Let's say there were 100 packages

For 60 packages,45 packages per hour

Time taken in 60 packages

$\frac{60}{45}=\frac{4}{3} hour$

For 40 packages, 12 package per hour

Time taken in 40 packages

$\frac{40}{12}=\frac{10}{3} hour$

Total time taken $=\frac{4}{3}+\frac{10}{3}=\frac{14}{3}hour$

Total packages=100

Average rate$=\frac{100}{\frac{14}{3}}=\frac{100×3}{14}$

$\frac{150}{7}$ Package /hour

Or 21.43 package /hour