Pre-Algebra

A machinist can produce 114 parts in 6 minutes. At this rate, how many parts can the machinist produce in 15 minutes?

Step-by-step solution with explanation

Final Answer

285 parts

Step-by-step solution

1

Find the rate of parts per minute

We divide the total parts by the total time to find how many parts are made each minute. This gives us the unit rate.
2

Set up the proportion for 15 minutes

We set up a proportion where x is the unknown number of parts in 15 minutes. Both ratios must be equal since the rate stays the same.
3

Cross-multiply to solve for x

Cross-multiplying means we multiply the numerator of one fraction by the denominator of the other. This clears the fractions and gives us a simple equation.
4

Divide both sides to find x

We divide both sides by 6 to isolate x. This tells us the total number of parts produced in 15 minutes.

Understanding this problem

Learning Insight

This is a direct proportion problem. When two quantities increase at the same rate (like time and parts made), you can always scale one ratio up or down to find the missing value. The unit rate (parts per minute) is the constant that ties them together.

Quick Tip

Find the unit rate first, then just multiply: 19 parts/min × 15 min = 285. This one-step shortcut is faster than setting up a full proportion every time.

Common Mistake

Students sometimes flip the ratio — putting minutes on top and parts on bottom — which gives a nonsense decimal answer. Always keep the same quantity in the same position on both sides of the proportion.