Question

1. a 155 - pound person burns about 500 calories per hour playing racquetball.

a. one pound is equal to 3500 calories. how long will it take to burn 1 pound playing racquetball?
b. how long will it take to burn 5 pounds playing racquetball? explain your reasoning.
c. if the person were to rest 5 minutes every 30 minutes of playing, how long would it take to burn 1 pound?

Explanation:

Step1: Calculate time to burn 1 - pound for part a

We know the rate of calorie - burning is 500 calories per hour and 1 pound = 3500 calories. Use the formula $t=\frac{C}{r}$, where $C$ is the total calories and $r$ is the rate of calorie - burning.
$t=\frac{3500}{500}=7$ hours

Step2: Calculate time to burn 5 - pounds for part b

Since it takes 7 hours to burn 1 pound, to burn 5 pounds, we multiply the time for 1 pound by 5.
$t = 7\times5=35$ hours

Step3: Calculate effective playing time per 35 - minute cycle for part c

The person plays for 30 minutes and rests for 5 minutes in a 35 - minute cycle. The rate of calorie - burning during playing is 500 calories per hour. In 30 minutes (0.5 hours), the number of calories burned per cycle is $500\times0.5 = 250$ calories.

Step4: Calculate number of cycles to burn 1 pound for part c

Since 1 pound is 3500 calories, the number of 35 - minute cycles $n=\frac{3500}{250}=14$ cycles.

Step5: Calculate total time to burn 1 pound for part c

Each cycle is 35 minutes, so the total time $T=14\times35 = 490$ minutes. Convert 490 minutes to hours and minutes: $490\div60 = 8$ hours and 10 minutes.

Answer:

a. 7 hours
b. 35 hours. Reason: Since it takes 7 hours to burn 1 pound, to burn 5 pounds, we multiply the time for 1 pound by 5.
c. 8 hours and 10 minutes