Mary and janet are running in the apple hill fun run. mary runs at 7 mph. janet at 5 mph. if they start at the same time, how long will it be before they are 1.5 miles apart?

The important factor here is the relative difference in speed between the two runners. Mary is running 2 miles an hour faster than Janet, so in effect from Janet's reference frame the gap grows as if she is standing still and Mary is running at 2 miles per hour. Therefore, to determine when the gap will grow to 1.5 miles we take 1.5 miles and divide it by 2 miles/hour to yield 0.75. Thus it will be 0.75 hours, or 45 minutes, before the two are 1.5 miles apart.

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