Question

Suppose that a family's two cars produce a combined rate of 50 grams per kilometer of carbon dioxide pollution. During one day last week, the first car drove 40 kilometers and the second drove 25 kilometers. the two cars produced a combined total of 1775 grams of carbon dioxide pollution. At what rate does each car produce carbon dioxide pollution?

Answer 1

By setting up a system of equations, we can determine that the first car's rate of carbon dioxide pollution is 35 grams/km, and the second car's rate is 15 grams/km.

Step-by-step explanation:

To solve for the rate of carbon dioxide pollution for each car, we need to set up a system of equations based on the information given. We know the total combined pollution and the distances each car traveled.

First, let's assume the first car's rate of CO2 pollution is r1 grams per kilometer, and the second car's rate is r2 grams per kilometer. Then we have the following system of equations:

1. 40r1 + 25r2 = 1775 (Total CO2 pollution)
2. r1 + r2 = 50 (Combined rate of pollution)

We can solve these equations using the substitution or elimination method. Let's use substitution.

From equation (2), r2 = 50 - r1. Substituting this into equation (1), we get:

• 40r1 + 25(50 - r1) = 1775
• 40r1 + 1250 - 25r1 = 1775
• 15r1 = 525
• r1 = 35 grams/km (Rate of pollution for the first car)

Now, plug r1 into equation (2) to find r2:

• r2 = 50 - 35
• r2 = 15 grams/km (Rate of pollution for the second car)

Therefore, the first car's pollution rate is 35 grams/km and the second car's rate is 15 grams/km.