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.

Question

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?
1.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.
2.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.
3.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.
4.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.

Answer 1

The correct statement is:

3. 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.

Mark accurately calculates the unit rate of houses delivered per minute and then uses that rate to find the number of houses that can be delivered in 7.5 minutes. Even though the mail carrier delivers to whole houses, the calculation of the unit rate (1.2 houses per minute) is still valid as a way to estimate how many houses can be delivered to over a specified time period. Therefore, based on Mark's calculation, in 7.5 minutes, the carrier can deliver to approximately 9 houses.