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In our example, the steps are:

  1. Distance is the same for both women.
  2. Choose x = Barbara's rate (in mph). Bonnie's rate (in mph) = x + 15
  3. Barbara's distance: d = rt = x(2) = 2x
  4. Bonnie's distance: d = rt = (x + 15)(1.5) = 1.5x + 22.5
  5. 2x = 1.5x + 22.5
  6. x = 45


Barbara travels at 45 miles per hour. Bonnie travels at 60 miles per hour.

Here is another example:

Jeff and Jed are twins who run at exactly the same speed. 45 minutes after they begin running, Jeff pulls a muscle and has to stop. Jed finishes the run -- 4 more miles. If Jed runs for 75 minutes total, how many miles did Jeff run before he stopped?

  1. Rate is the same for both men.
  3. Choose x = Jeff's distance. Jed's distance = x + 4
  4. Jeff's rate: r = =
  5. Jed's rate: r = =
  6. =
  7. x = 6


Jeff ran 6 miles.

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