Question 11 • HCISD-Mathematical Models with Applications B-CR SUMMER
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses. Which statement is correct?
Answer
A
Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.
B
Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.
C
Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
D
Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
Explanation
Divide 36 houses by 30 minutes to find the rate: 36 ÷ 30 = 1.2 houses per minute. A unit rate can be fractional; it describes the average delivery rate, not a claim that the carrier finishes exactly 1.2 houses in one minute. Multiplying 1.2 houses per minute by 7.5 minutes gives 9 houses, so Mark’s method is correct. Choice C states this reasoning.
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