1. During 60mi of city driving, Jenna averaged 15mi/gal. She then drove 140mi on an expressway and averaged 25mi/gal for the entire 200mi. Find the average fuel consumption on the expressway.

2. The excursion boat Holiday travels 35km upstream and then back again in 4h 48min. If the speed of the Holiday in still water is 15km/h, what is the speed of the current?

3. Members of the Computer Club were assessed equal amounts to raise $1200 to buy some software. When 8 new members joined, the per-member assessment was reduced by $7.50. What was the new size of the club?

1. Ave(city) = 15 mi/gal,

Ave(exp.) = x mi/gal,

Ave = (15 + x) / 2 = 25 mi/gal,
Multiply both sides by 2 and get:
15 + x = 50,
x = 50 - 15,
x = 35 mi/gal, express way.

2. d = 2 * 35 km = 70 km,
Speed = 70 km / 4.8h = 14.58 km/h in
still water,

C = 15 - 14.58 = 0.417 km/h Current
speed.

3. x = old membership size,
x + 8 = new membership size,

1200 / x = assessment under old membership,
1200 / (x + 8) = assessment under new
membership,

1200 / (x + 8) = ( 1200 / x ) - 7.50,
1200 / (x + 8) - 1200 / x = -7.50,

common denominator = x(x + 8),
(1200x - 1200(x + 8)) / x(x + 8) = -7.5

(1200x - 1200x - 9600) / x(x + 8) = -7.50,
-9600 / x(x + 8) = -7.50,
Cross multiply:
-7.50 * x(x + 8) = -9600,
Divide both sides by -7.50 and get:
x(x + 8) = -9600 / -7.50,
x^2 + 8x = 1280,
x^2 +8x - 1280 = 0,
Factor Eq and get:
(x - 32) (x + 40) = 0,
x - 32 = 0,
x = 32,

x + 40 = 0,
x = -40.
Solution set: x = 32, and x = -40.
select pos. value: x = 32.

x + 8 = 32 + 8 = 40 = new membership.

Correction:

14.58 km/h is NOT still wqater.

1. To find the average fuel consumption on the expressway, we need to calculate the total fuel used and divide it by the distance traveled on the expressway.

Let's break this down step by step:
- In city driving, Jenna averaged 15 miles per gallon (mpg) over 60 miles. So, she used 60 miles / 15 mpg = 4 gallons of fuel in the city.
- After city driving, she drove 140 miles on the expressway and averaged 25 mpg for the entire 200 miles. So, she used 200 miles / 25 mpg = 8 gallons of fuel in total.
- To find the fuel consumption on the expressway, we subtract the fuel used in the city from the total fuel used on the 200-mile trip. Thus, the fuel consumed on the expressway is 8 gallons - 4 gallons = 4 gallons.

Therefore, Jenna's average fuel consumption on the expressway is 4 gallons.

2. To find the speed of the current, we need to calculate the speed of the excursion boat in still water. We can then use this information to determine the speed of the current.

Let's solve this step by step:
- The excursion boat travels 35 km upstream and back in a total of 4 hours and 48 minutes, which is 4 + 48/60 = 4.8 hours.
- Since the distance traveled upstream and downstream is the same, the boat's total distance is 35 km + 35 km = 70 km.
- If we let the speed of the boat in still water be v km/h and the speed of the current be c km/h, then the time taken to travel upstream is (35 / (v - c)) hours, and the time taken to travel downstream is (35 / (v + c)) hours.
- Therefore, we can set up the equation: (35 / (v - c)) + (35 / (v + c)) = 4.8.
- To solve this equation, we can multiply both sides by the least common denominator (v - c)(v + c), which simplifies to:
35(v + c) + 35(v - c) = 4.8(v - c)(v + c).
- Simplifying further, we get: 70v = 4.8(v^2 - c^2).
- Expanding and rearranging, the equation becomes: 4.8v^2 - 70v - 4.8c^2 = 0.
- This equation can be solved using the quadratic formula. However, since we are only interested in the speed of the current, we can disregard the value of v and focus on the value of c.
- Solving the equation for c, we find that the speed of the current is approximately 3.9 km/h.

Therefore, the speed of the current is approximately 3.9 km/h.

3. To find the new size of the club, we need to determine the original number of members and then calculate the new number of members after 8 new members joined.

Let's solve this step by step:
- Let's assume the original number of club members is x.
- Each member was assessed an equal amount to raise $1200, so the per-member assessment is 1200 / x dollars.
- When 8 new members joined, the per-member assessment was reduced by $7.50, so the new per-member assessment is (1200 / x) - 7.50 dollars.
- From this information, we can set up the equation: (1200 / x) - 7.50 = (1200 / (x + 8)).
- To solve this equation, we can multiply both sides by (x)(x + 8), which simplifies to:
1200(x + 8) - 7.50(x)(x + 8) = 1200(x).
- Expanding and rearranging, the equation becomes: 9600 - 7.50x^2 - 60x = 1200x.
- Simplifying further, we get: 7.50x^2 + 1260x - 9600 = 0.
- This equation can be solved using the quadratic formula or factoring. Let's use factoring:
We can divide each term by 7.50 to simplify the equation: x^2 + 168x - 1280 = 0.
- Factoring, we can rewrite the equation as (x + 40)(x - 32) = 0.
- Setting each factor equal to zero, we find that x = -40 or x = 32.
- Since the number of members cannot be negative, we can disregard the solution x = -40.
- Therefore, the original number of club members was 32.
- When 8 new members joined, the new size of the club is 32 + 8 = 40 members.

Therefore, the new size of the club is 40 members.

To find the answer to the first question, we need to calculate the average fuel consumption on the expressway. We know that Jenna drove 60 miles in the city and averaged 15 miles per gallon. This means that she used 60 miles / 15 miles per gallon = 4 gallons of fuel during city driving.

Next, we need to find out how much fuel Jenna used on the expressway. We know that she drove 200 miles in total and averaged 25 miles per gallon for the entire distance. This means that she used 200 miles / 25 miles per gallon = 8 gallons of fuel in total.

To find the amount of fuel used on the expressway, we subtract the fuel used during city driving from the total fuel used: 8 gallons - 4 gallons = 4 gallons.

Therefore, Jenna used 4 gallons of fuel on the expressway. This gives us an average fuel consumption of 4 gallons / 140 miles = 1 gallon per 35 miles on the expressway.

For the second question, to find the speed of the current, we can use the formula:

Speed in still water = (Speed downstream + Speed upstream)/2

In this case, we know that the speed of the Holiday in still water is 15 km/h. Since the distance traveled upstream and downstream is the same (35 km each), we can use the time traveled to find the speed.

The total time traveled is given as 4 hours and 48 minutes. We need to convert this to hours, so we have 4 hours + 48 minutes/60 = 4.8 hours.

Now, we can calculate the speed downstream using the formula:

Speed downstream = (Distance traveled downstream)/(Time taken downstream)

Since the speed downstream is the speed of the boat in still water plus the speed of the current, we have:

Speed downstream = Speed in still water + Speed of current

For the upstream journey, the speed of the boat in still water is reduced by the speed of the current, so:

Speed upstream = Speed in still water - Speed of current

Solving both equations, we have:

15 km/h + Speed of current = (35 km)/(4.8 hours)

15 km/h - Speed of current = (35 km)/(4.8 hours)

Multiplying both equations by 4.8 hours and simplifying, we get:

72 + 4.8 * Speed of current = 35

72 - 4.8 * Speed of current = 35

Solving for Speed of current, we find:

Speed of current = (72 - 35)/(4.8)

Therefore, the speed of the current is 7.29 km/h (rounded to two decimal places).

For the third question, let's assume the original size of the club was x members. Each member was assessed an equal amount to raise $1200, so the assessment per member would be $1200 / x.

When 8 new members joined, the per-member assessment reduced by $7.50. This means the new per-member assessment is now $1200 / (x + 8) = ($1200 / x) - $7.50.

To solve this equation, we start by multiplying both sides by x * (x + 8) to eliminate the denominators:

$1200 * (x + 8) = $1200 * x - $7.50 * x * (x + 8)

Expanding and simplifying the equation:

1200x + 9600 = 1200x - 7.50x^2 - 60x

Rearranging the equation:

7.50x^2 + 60x - 9600 = 0

To find the new size of the club, we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula.

Factoring the quadratic equation, we get:

7.50(x - 20)(x + 64) = 0

This gives us two possible solutions:

x - 20 = 0 or x + 64 = 0

x = 20 or x = -64

Since the number of members cannot be negative, the new size of the club is 20 members.