Writing Equations and Functions from Word Problems

You are managing a small assembly operation building toy cars. Due to increased demand, you need to hire an employee in addition to the two that are already building this line of toy assemblies. For the questions below, show all your work in deriving the answer (Total: 4 pts).

a. Write a function for the time, T, that will be required for three employees to build N toy cars if it takes each of them t1, t2, and t3 minutes to build the N cars separately. Show any intermediate steps in deriving the formula (1 pt)

b. Rewrite the formula to calculate t3 given T, t1, and t2. (1pt)

c. From your formula in (b), what will the new assembler's (#3) time need to be for T = 7.2 minutes , t1 = 20 minutes , and t2 = 25 minutes ? Answer with one decimal place. (1 pt)

d. If N=15 toys, how many toy cars can employee #3 build per minute, given his time in (c)? (1 pt)

Solution Preview

Hello!
Here are your answers.

Question a
Consider employee #1. He can build N cars in t1 minutes. That means he can build N/t1 cars per minute. Then the same is true for the other employees: employee #2 can build N/t2 cars per minute and employee #3 can build N/t3 cars per minute. This means that, if the three of them work at the same time, they can build:

(N/t1 + N/t2 + N/t3) cars per minute

Let's now find how many minutes they need per car. This is just the ...

Solution Summary

Equations are written from a word problem. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

... o For non-integer answers, please write your answer ... hyperbola, or exponential), explain in your works, why you ... slope-intercept form of the equation, give one ...

... Complete solutions are written with the help of equation... 74- Page 462 Exercise 74- 462 Write a system ... $1.45 for four books and 3 magazines, Writing in equation...

Basic Algebra and Word Problems. ...Write equations for the vertical and the horizontal lines passing through ... water bill (in dollars) is a linear function of the ...

... b.) Use the function to predict the test score of someone who has studied for 18 hours. ... 16. Define your variable and write an equation that could be used to ...

... d. For what value is this equation undefined ... http://www.seaworld.org/animal-info/ info-books/flamingo/physical ... a. Write an expression that gives the total cost to ...

... f) Find the equation of the Vertical Asymptote: We ...Write the following statement in logarithmic form: 10 2 = 2 ... The logarithmic form has the base written to the ...

... This equation is undefined for x = 100% since we ... www.seaworld.org/animal-info/info- books/flamingo/physical ...Write the expression that gives the average cost per ...

Exercises. Section 2.1: Exercise 96 Solve each problem by writing and solving an equation. 96. ... Identify the variable and write an equation that describes ...

... of a town is modeled by the equation P (t ... 7. 3 1. a. Write 4 = 64 in logarithmic form. x The exponential function is y = b . The corresponding logarithmic ...

...Write quadratic equations for which ... As we saw in problem 17, a quadratic function with roots (solutions) x0 and x1 can be written as: y = ( x − x0 ...