Question

1. a postal carrier can deliver to 130 houses in a 2.5-hour period. at this rate, how many hours will it take to deliver to 312 houses?

Explanation:

Step1: Find the delivery rate per hour

The postal carrier delivers to 130 houses in 2.5 hours. So the rate \( r \) (houses per hour) is calculated by dividing the number of houses by the time. So \( r=\frac{130}{2.5} \). Calculating that, \( \frac{130}{2.5} = 52 \) houses per hour.

Step2: Calculate time for 312 houses

We know the rate is 52 houses per hour. Let \( t \) be the time (in hours) to deliver to 312 houses. Using the formula \( \text{Number of houses} = r\times t \), we can rearrange it to \( t=\frac{\text{Number of houses}}{r} \). Substituting the values, \( t = \frac{312}{52} \). Calculating that, \( \frac{312}{52}=6 \).

Answer:

6