Answer:
(d) 0.9 ft/min
Explanation:
You want the unit rate associated with the trencher if it digs a 36 ft trench in 40 minutes, and a 58.5 ft trench in 65 minutes.
Proportion
The length of the trench is proportional to the time if the ratio length/time is constant. For the two given trench lengths, that ratio is ...
(36 ft)/(40 min) = 0.9 ft/min
(58.5 ft)/(65 min) = 0.9 ft/min
The slope of the equation relating length to time is the constant value 0.9 ft/min, choice D.
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Additional comment
When time is involved, we usually want rates expressed per unit time. This puts minutes in the denominator.
However, the "unit rate" can also be expressed with 1 foot as the unit. The rate expressed that way is 1.11 min/ft, choice B.
Which of these you choose will depend on the application of the formula. If you know you want to dig a 36 ft trench, this tells you the time it will take is (1.11 min/ft)·(36 ft) ≈ 40 minutes.
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