Question

Calculate the unit rate for Machine A and Machine B. Determine which is the greater rate (Below).

Machine A covers 5/8 square feet in 1/4 hour or Machine B covers 2/3 square feet in 1/5 hour.

Answer 1

Unit Rate of Machine A = 2.5 square feet per hour

Unit Rate of Machine B = 3.333 square feet per hour.

The unit rate of Machine B is greater than unit rate of machine A.

Explanation:

The unit rates for both machines need to be calculated first.

The unit rate will be calculated as:

`Unit\ rate = (Area\ covered)/(Time)`

For Machine A:

Area Covered = 5/8

Time = 1/4

The unit rate will be:

`U_A = ((5)/(8) )/((1)/(4) ) \\Using\ rule => ((a)/(b) )/((c)/(d) ) = (a)/(b) * (d)/(c)\\=(5)/(8) * 4 \\= (5)/(2) = 2.5\ square\ feet\ per\ hour`

For Machine B:

Area Covered = 2/3

Time = 1/5

`U_B = ((2)/(3))/((1)/(5))\\= (2)/(3) * \frac{5}\\= (10)/(3)\\= 3.33...\ square\ feet\ per\ hour`

As it can be seen that unit rate for Machine B is greater than Unit Rate of Machine A.

Hence,

Unit Rate of Machine A = 2.5 square feet per hour

Unit Rate of Machine B = 3.333 square feet per hour.

The unit rate of Machine B is greater than unit rate of machine A.