Question

Each week you spend a total of 5 hours exercising. You swim part of the time and bike the rest. Swimming burns 300 calories per hour and biking burns 440 calories per hour.

A. Write a rule (equation) for the total amount of calories you burn for the whole 5 hours as a function of the time you spend swimming.

B. One week you spend half the time swimming. How many calories do you burn during the whole 5 hours?​

Answer 1

The equation for the total amount of calories burned as a function of the time spent swimming is y = 300x + 440(5 - x). If you spend half the time swimming, you will burn 1410 calories during the whole 5 hours.

Step-by-step explanation:

A. To write a rule (equation) for the total amount of calories burned for the whole 5 hours as a function of the time spent swimming, we'll use the variables:

x: Time spent swimming (in hours)

y: Total amount of calories burned

Since each hour of swimming burns 300 calories, and the remaining time is spent biking, which burns 440 calories per hour, we can write the equation:

y = 300x + 440(5 - x)

B. If you spend half the time swimming, which is 2.5 hours, substitute this value into the equation to find the total amount of calories burned:

y = 300(2.5) + 440(5 - 2.5)

Simplifying this equation:

y = 750 + 660

y = 1410

Therefore, you will burn 1410 calories during the whole 5 hours.