Concept 7

Solve multistep problems by combining proportions, rates, and unit conversions.

Core Idea

For multistep rate problems, chain the conversions in one expression. Each fraction eliminates one unit and introduces the next. The final unit standing is your answer's unit.

Understanding

Chain the units. Handle one conversion at a time so every intermediate unit cancels.

  1. Start with the given rate.
  2. Multiply by each conversion factor in a way that cancels the unwanted unit.
  3. Keep going until only the target unit remains.
  4. Check the final unit before you stop.

The SAT often nests a rate, a time, and another conversion in one problem. Do the algebra in stages, not all at once.

Step by Step

  1. List all the rates and conversions given in the problem.
  2. Identify the starting unit and the target unit.
  3. Arrange conversion fractions so each step cancels the previous unit.
  4. Multiply across — cancel units first, then compute.
  5. Verify the final unit matches what the question asks for.

Misconceptions

  • Skipping a conversion step, leaving an intermediate unit in the answer.
  • Multiplying when you should divide (or vice versa) because a fraction is flipped.
  • Rounding intermediate steps, which compounds errors in multi-step chains.
Question

Worked Example

A water tank fills at a rate of 3 gallons per minute. There are 4 quarts in a gallon and 2 pints in a quart. How many pints of water flow into the tank in 15 minutes?

Select an answer to see the explanation