Question

Jack and Jill work out together. Jack starts at 160lbs and gains 2lbs per week. Jill starts at 200lbs and loses 0.5 pounds per week. How many weeks until Jack and Jill weigh the same?

Answer 1

By setting up linear equations for Jack and Jill's weights over time and solving for when the equations are equal, we find that it will take 16 weeks for both Jack and Jill to weigh the same.

Step-by-step explanation:

To solve the problem of when Jack and Jill will weigh the same, we use linear equations to represent their respective weights over time. Let's assume 'w' is their weight and 't' is the number of weeks. For Jack, the equation is w = 160 + 2t because he starts at 160lbs and gains 2lbs each week. For Jill, the equation is w = 200 - 0.5t because she starts at 200lbs and loses 0.5lbs each week.

To find the number of weeks until Jack and Jill weigh the same, we set the two equations equal to each other:

1. 160 + 2t = 200 - 0.5t
2. Add 0.5t to both sides: 160 + 2.5t = 200
3. Subtract 160 from both sides: 2.5t = 40
4. Divide both sides by 2.5: t = 16

Therefore, it will take 16 weeks for Jack and Jill to weigh the same.