Timothy drove at an average speed of 10 mph for some time and then at an average speed of 50 mph for the rest of the journey. If he made no stops during the trip and his average speed for the entire journey was 40 mph, for what fraction of the total time did he drive at 50 mph? Choose the correct answer
A) 1/5 B) 1/3 C) 2/5 D) 3/4 E) 3/5
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 journey was 40 mph, then he drove at 50 mph for a longer duration of time.   10 30   10--40------50   This shows that you can divide the entire journey into 4 equal parts. Thus, 3/4 part he drove at 50 mph and 1/4 part he drove at 10 mph.   Answer: 3/4
<result>D</result>
Timothy drove at an average speed of 10 mph for some time and then at an average speed of 50 mph for the rest of the journey. If he made no stops during the trip and his average speed for the entire journey was 40 mph, for what fraction of the total time did he drive at 50 mph?