A family has two cars. During one particular week, the first car consumed 40 gallons of gas and the second consumed 15 gallons of gas. The two cars drove a combined total of 1575 miles, and the sum of their fuel efficiencies was 55 miles per gallon. What were the fuel efficiencies of each of the cars that week?

Fuel efficiency of first car = 30 miles/gallon

Fuel efficiency of second car = 25 miles/gallon

Step-by-step explanation:

Given that:

Fuel consumed by first car = 40 gallons

Fuel consumed by second car = 15 gallons

Total distance drove by the two cars combined = 1575 miles

Sum of their fuel efficiencies = 55 miles/gallon

To find:

The fuel efficiencies of each of the cars = ?

Solution:

Fuel efficiency of a car is defined as the ratio of distance traveled in miles to the number of gallons used by the car.

Let the distance traveled by first car = miles

So, the distance traveled by other car = (1575 - ) miles

Fuel efficiency of first car = miles/gallon

Fuel efficiency of second car = miles/gallon

As per given question statement:

Distance traveled by first car = 1200 miles

Fuel used by first car = 40 gallons

So, fuel efficiency of first car =

Distance traveled by second car = 1575 - 1200 = 375 miles

Fuel used by second car = 15 gallons

So, fuel efficiency of second car =

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

good job you smart son of a gun you are smarter that einstein. 7