Question

reminder: complete hw on looseleaf with a proper heading. show all work. (even for m/c questions) write your # in the top right corner of the paper. homework 3.18 1. a high speed elevator can rise 480 feet in 30 seconds. which expression represents the rate, in feet per minute, of the elevator? a. 480 x 30 b. 480 ÷ 30 c. 480 x 2 d. 480 ÷ 2 1. a group of students organized a car wash to raise money for a local charity. the students charged $5.00 for each car they washed. in 3 hours, they washed 12 cars. at that rate, how much money could they earn from washing cars for 10 hours? 1. darnell’s car used 8 gallons of gasoline to travel 340 miles. after a mechanic world on the car, it used 7 gallons to travel 350 miles. if the price of gasoline is approximately $4.00 per gallon, how much less, to the nearest cent per mile, did it cost to run the car after the mechanic worked on it? 1. a recipe calls for 2 cups of sugar and 10 cups of water. how much sugar is used per cup of water? homework 3.18 continued 5. mr tola has a piece of wood that is 8 ¼-feet in length. he wants to cut it into pieces that are each ¾-foot in length. how many ¾-foot pieces of wood can mr. tola make? a. 7 b. 8 c. 9 d. 11

Explanation:

First Question (Elevator Rate)

Step1: Convert seconds to minutes

30 seconds is $\frac{30}{60} = 0.5$ minutes, or we can think that 1 minute has 2 intervals of 30 seconds. So to find the rate in feet per minute, if in 30 seconds (0.5 minutes) it rises 480 feet, then in 1 minute (which is 2 times 30 seconds), the distance would be $480\times2$ (because 1 minute is 2 * 30 seconds, so we multiply the distance in 30 seconds by 2 to get per minute). Alternatively, the rate in feet per second is $480\div30$, and to convert to feet per minute, we multiply by 60: $(480\div30)\times60 = 480\times2$. So the correct expression is $480\times2$.

Step2: Analyze options

• Option a: $480\times30$ is incorrect as it would overstate the rate.
• Option b: $480\div30$ is feet per second, not per minute.
• Option c: $480\times2$ is correct as shown.
• Option d: $480\div2$ is incorrect.

Step1: Find the rate of cars washed per hour

In 3 hours, 12 cars are washed, so cars per hour is $12\div3 = 4$ cars per hour.

Step2: Find number of cars washed in 10 hours

Cars in 10 hours: $4\times10 = 40$ cars.

Step3: Calculate total money earned

Each car is $5, so total money is $5\times40 = 200$ dollars.

Step1: Cost per mile before mechanic

Gallons used: 8, miles: 340, cost per gallon: $4. Total cost: $8\times4 = 32$ dollars. Cost per mile: $\frac{32}{340}\approx0.0941$ dollars per mile.

Step2: Cost per mile after mechanic

Gallons used: 7, miles: 350, total cost: $7\times4 = 28$ dollars. Cost per mile: $\frac{28}{350}= 0.08$ dollars per mile.

Step3: Find the difference

Difference: $0.0941 - 0.08 = 0.0141\approx0.01$ dollars per mile (to the nearest cent).

Answer:

c. $480\times2$

Second Question (Car Wash Earnings)