Rates and work
Scale a rate — workers, speed, cost per unit — up or down to a new quantity.
What a rate is
A rate tells you how much happens per unit of something else — kilometres per hour, items per minute, cost per kilogram.
Get to "per one" and the rest is easy
4 machines fill 200 bottles in 5 minutes. How many bottles would 6 machines fill in 5 minutes?
Work down to one machine: 200 ÷ 4 = 50 bottles per machine. Then up: 6 × 50 = 300.
This "down to one, then up" method handles almost every rate question you will meet.
Watch which quantity changes
If the time also changes, deal with one variable at a time — machines first, then minutes. Trying to do both at once is where mistakes creep in.
How to attack this question type
- 1
Always reduce to "per one" first — per machine, per hour, per person. Then scale up to what is asked.
- 2
Change one thing at a time. If both the number of workers and the time change, do them in two steps.
- 3
More workers means LESS time; faster speed means LESS time. If your answer went the wrong direction, you multiplied where you should have divided.
- 4
Sanity-check the size of your answer. If six machines produce less than four did, something is wrong.
Practice · untimed
Six printers produce 240 pages in 4 minutes. At the same rate, how many pages would nine printers produce in 4 minutes?
More in Numerical Reasoning
Number sequences
Find the missing term by working out the rule that generates the sequence.
Ratio and proportion
Share a quantity in a given ratio, or scale one quantity against another.
Age problems
Relate two ages now and at another time, then solve for one of them.
Sequences — missing number
Pairs or a small grid follow one rule; work the rule out and fill in the hidden number.
Sequences — find the rule
A run of numbers was built by one rule; choose the written rule that fits every step.
Sequences — odd one out
Every number is shown and one of them breaks the pattern the rest follow; find it.