A car traveled the first quarter of a certain distance at six times the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?
Choose the correct option
A) 1/14  B) 1/15  C) 1/16  D) 1/17  E) 1/19
These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be one sixth, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 1 2/3 km/h for the remaining quarters.   He'll take 1 hour to do the first quarter and then 6 hours for the second quarter, 6 hours for the third and 6 hours for the fourth. On total he will take 19 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/19. Answer 1/19.
<result>E</result>
A car traveled the first quarter of a certain distance at six times the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?