SAT problem solving rates questions

Rate of work: Definition

Rate of work measures the speed at which a task is completed, often expressed as tasks per hour.

If a car travels 120 miles in 2 hours, rate?

Rate = Distance/Time = $\displaystyle \\frac{120}{2} = 60$ miles per hour.

True or false: Rate is always constant.

False, because rates can change depending on conditions.

Difference between speed and rate.

Speed is a scalar quantity, while rate often involves comparison of two quantities.

Fill in the blank: A gardener can plant 30 flowers in 3 hours. His rate is ____ flowers/hour.

$\displaystyle \\frac{30}{3} = 10$ flowers per hour.

Rate of production: Example

If a factory produces 200 widgets in 4 hours, the rate is 50 widgets per hour.

True or false: Adding rates is possible if tasks are independent.

True, because independent rates can be summed to find a combined rate.

What is the combined rate if two people work together?

Combined rate = Rate of person A + Rate of person B.

If a job takes 8 hours for one worker, how long for two?

Two workers can complete the job in 4 hours; their combined rate is double.

Question: A bike travels 90 miles in 3 hours. What is its speed?

Speed = $\displaystyle \\frac{90}{3} = 30$ miles per hour.

Fill in the blank: The rate of typing is 40 words/minute. In 5 minutes, a typist types ____ words.

40 words/minute × 5 minutes = 200 words.

Difference between average speed and instantaneous speed.

Average speed is total distance over total time; instantaneous speed is speed at a specific moment.

If a train travels 240 miles in 4 hours, what's the rate?

Rate = $\displaystyle \\frac{240}{4} = 60$ miles per hour.

True or false: Rate problems require simultaneous equations.

False, they often can be solved with simple division and addition.

If it takes 10 hours to paint a house, how long for 5 painters?

5 painters can complete the job in 2 hours; rate increases with more workers.