Hannah and Jake race around a running track. Hannah runs at a constant rate of one lap every 2 minutes and Jake runs at a constant rate of one lap every 5 minutes. If they both start at the same time, how many minutes will it take for Hannah to get exactly one lap ahead of Jake? Choose the correct choice from the following options: A) 3/5 B) 5/3 C) 7/3 D) 10/3 E) 10/7
Let x be the number of minutes it takes for Hannah to get one lap ahead.   Then Hannah ran x/2 laps and Jake ran x/5 laps.   x/2 = 1+x/5   5x=10+2x   3x=10   x=10/3   The answer is 10/3.
<result>D</result>
Hannah and Jake race around a running track. Hannah runs at a constant rate of one lap every 2 minutes and Jake runs at a constant rate of one lap every 5 minutes. If they both start at the same time, how many minutes will it take for Hannah to get exactly one lap ahead of Jake?