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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

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.