Hi All,

We're told that Tim and Glenn are running laps around a circular track and that they start at exactly the same time. We're asked in how many seconds will have passed when Tim has run exactly one lap further than Glenn.

This is an example of a rare 'combined rate' question (sometimes called a "chase down" question). The key to these types of questions is to figure out the DIFFERENCE in speeds of the two entities (when they're moving at the same time) and use that number as a basis for comparison.

1) Tim runs each lap in 48 seconds and Glenn runs each lap in 60 seconds.

Here, we know that Tim runs a lap in 48 seconds and Glenn runs a lap in 60 seconds. The difference in their rates is 12 seconds/lap.

Tim will "catch up" 12 seconds on Glenn every lap. Since Glenn needs 60 seconds to finish a lap, Tim needs 60/12 = 5 laps to catch Glenn.

You can see that the results are correct by doing the following math:

Tim: (5 laps)(48 seconds per lap) = 240 seconds

Glenn: (X laps)(60 seconds per lap) = 240 seconds

X = 240/60 = 4 laps

In 240 seconds, Tim runs 5 laps and Glenn runs 4 laps. At this point, Time has "lapped" Glenn.

Fact 1 is SUFFICIENT

2) The track is 400 meters in circumference.

The information in Fact 2 tells us nothing about the two rates, so there's no way to answer the question.

Fact 2 is INSUFFICIENT

Final Answer:

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Rich

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