Comparing rates in words, step by step

Which is faster, 60 miles in 5 hours or 84 miles in 7 hours?

The question
Ay = 11x, y liters and x minutesB65 liters in 5 minutesAB

Which is greater?

A y = 11x, y liters and x minutes B 65 liters in 5 minutes

Ay = 11x, y liters and x minutes
B65 liters in 5 minutes
y = 11x, y liters and x minutes11 per minute
65 ÷ 5=13 per minute
A 11B 13
greater:B
  1. These two are written in different ways, so there is nothing to compare yet — the numbers on the page are not the same kind of number. Turn each one into a rate PER ONE minute first, and do not look at which looks bigger until you have.
  2. A: the number in front of x, which is already a rate per one minute: 11. So A is 11 liters per minute.
  3. B: 65 ÷ 5 = 13. So B is 13 liters per minute.
  4. Now they can be compared: A is 11 and B is 13 per minute, so B is greater.

How it works.

  1. 01

    These two are written in different ways, so there is nothing to compare yet — the numbers on the page are not the same kind of number. Turn each one into a rate PER ONE minute first, and do not look at which looks bigger until you have.

  2. 02

    A: the number in front of x, which is already a rate per one minute: 11. So A is 11 liters per minute.

  3. 03

    B: 65 ÷ 5 = 13. So B is 13 liters per minute.

  4. 04

    Now they can be compared: A is 11 and B is 13 per minute, so B is greater.