Patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon. If she made no stops during the run and her average speed for the entire marathon was 5 mph, for what fraction of the total time did she run at 3 mph? Choose the correct choice from the following: A) 1/5 B) 2/3 C) 2/5 D) 3/5 E) 1/3
We don't need to get into calculations for solving this question. We can use the concept of weighted averages.   We know that if the average speed for the entire marathon was 5 mph, she ran at 6 mph for a longer duration.   2 1   3--5----6   This shows that you can divide the entire journey in 3 equal parts. Thus, 2/3 part she ran at 6 mph and 1/3 part she ran at 3 mph.   Answer: 1/3
<result>E</result>
Patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon. If she made no stops during the run and her average speed for the entire marathon was 5 mph, for what fraction of the total time did she run at 3 mph?