two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total 1075 of miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week?

Car 1 = 20 gallons

Car 2 = 25 gallons.

Step-by-step explanation:

Given:

Car 1

Efficiency, E1 = 35 miles per gallon

Car 2

Efficiency, E2 = 15 miles per gallon

Total Distance = D1 + D2

= 1075 miles

Total gas consumption = C1 + C2

= 45 gallons

Efficiency, E = distance, D/gas consumption, C

Let the gas consumption of car 1 and 2 be C1 and C2.

1. 1075 = 35 * C1 + 15 * C2

But C1 + C2 = 45

C1 = 45 - C2, into equation 1:

1075 = 35 * (45 - C2) + 15C2

500 = 20C2

C2 = 25 gallons

C1 = 20 gallons

The first car consumed 20 liters of fuel while the second consumed 25 liters of fuel

Step-by-step explanation:

In this question, we are told to calculate the number of gallons of fuels consumed by 2 cars given their underlying fuel efficiency values and the total number of distance travelled by these cars.

Firstly, we assign variables. Let the amount of fuel consumed by the first car be a while same consumed by the second car be b.

Now, from the question, we can deduce the following. They both went a total distance of 1075 miles. We translate this to an equation using a mix of their fuel efficiencies and their supposed fuel consumption in gallons.

This mathematically means:

35a + 15b = 1075 ... (I)

Total fuel consumed is 45 gallons. This means adding a and b gives 45

a + b = 45 ... ii

Solving both simultaneously, we can start from the position in ii where we can rewrite a as equals 45 - b I. e a = 45 - b. We then substitute this in I

35 (45-b) + 15b = 1075

1575-35b + 15b = 1075

20b = 500

b = 500/20 = 25

Recall a = 45 - b = 45-25 = 20