Question

A race pilot's average rate of speed over a 720-mile course is inversely proportional to the time in minutes t the pilot takes to fly a complete race course. The pilot's final score s is the average speed minus any penalty points p earned.

Write a function to model the pilot's score for a given t and p (Hint: d = rt)
Graph the function for a pilot who has two penalty points.
What is the maximum time a pilot with 2 penalty points can take to finish the course and still earn a score of at least 3?
2. How many milliliters of 0.30% sugar solution must you add to 75mL of 4% sugar solution to get a 0.50% sugar solution? Show your work.

3. Write three rational expressions that simplify to fraction numerator x plus 1 over denominator x minus 1 end fraction Click for more options

4. Explain the differences in the process of adding two rational expressions using the lowest common denominator (LCD) and adding them using a common denominator that is not the LCD. Include an example in your explanation.

Answer 1

Let’s start with the beginning

d = rt giving us
r = d/t when we solve for speed

Afternoon subtracting penalty points we get

score = d/t - p

Replace d with the distance

As the question states, graph for penalty = 2

For the calculation (max time for a penalty 2 and score 3, plug these values into the function and solve for t)

Answer 2

For the sugar question calculate how much sugar is already there by multiplying 75mL by 4 percent

Since we are adding a 0.30% solution we can find the amt of sugar added by letting x = volume of the 0.30% solution to get

(.3/100)x

Now, we want a 0.50% solution so

Total sugar/total volume = 0.5/100

= (0.04 * 75 + 0.3/100 * x)/(75+x) solve for x

Answer 3

For the third problem we want

(x+1)/(x-1) as the simplified result

To get a possible function that will reduce into this, simply multiply the numerator and denominator by the same quantity, such as

(x-7)(x+1)/((x-1)(x-7))

Answer 4

For the fourth problem, as long as the denominators are common they can still be added. However if the denominator is not the lcd there will still be simplifying to do at the end since there will be common factors between the numerator and denominator

Answer 5

For an example... how about

x/(x+1)+ x/(2x+2)

You can use the lcd 2x + 2 or a non-lcd like 4x + 4, the end result is the same but the non common lcd will require more simplifying at the end