# Rates

## Arithmetic: Rates

Read the following SAT test question and then select the correct answer.

Use the same method with each math question to avoid making mistakes.  Start by reading carefully and identifying the bottom line.  What question must you answer?  Then assess your options for answering the question, choosing the most time efficient method to attack the problem.  When you have an answer, loop back to verify that your answer matches the bottom line.

Machine X, working at a constant rate, can produce x bolts per hour. Machine Y, working at a constant rate, can produce x + 6 bolts per hour. In terms of x, how many bolts can both machines working together at their respective rates produce in 4 hours?

Bottom line: #bolts in 4 hr = ?

Assess your Options:  You could choose numbers for x and y and then see which of your answer choices matches the answer that you get, but you will still have to write an equation.  It will be much faster to leave the variable in the problem and write an equation to find the answer.

Attack the Problem:  You know that you have two machines, X and Y.  You know how much each of these machines produces in an hour.  Find out the total that they can produce in one hour.

X + Y (both machines)= x + x + 6          Combine like terms.
X + Y (both machines)= 2x + 6

In one hour you can produce 2x + 6 bolts.  However, your bottom line requires you to find the number of bolts that can be produced in 4 hours.  Multiply 2x + 6 by 4.

4(2x + 6)          Distribute the 4.
8x + 24

Loop Back:  You solved for 4 hours rather than just 1 hr, so you are ready to look at the answer choices.

(A) 4x + 12
(B) 4x + 24
(C) 6x + 30
(D) 8x + 24
(E) 8x + 36

The correct answer is (D).

On sat.collegeboard.org, 59% of the responses were correct.

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