SOLUTION: 2 friends go on a 4 day trip. on the first day they travel 1/4 of the total distance. on the second day they travel 1/2 of the remaining distance. They travel 2/3 of the remain dis

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Question 836046: 2 friends go on a 4 day trip. on the first day they travel 1/4 of the total distance. on the second day they travel 1/2 of the remaining distance. They travel 2/3 of the remain distance on the third day and complete the rest of the trip in the fourth day. On which day did they travel the greatest distance? And if they travel 12 km on the third day what is the total distance of the trip.
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the total distance of the trip
----------
1st day:
They traveled +%281%2F4%29%2Ad+ leaving +%283%2F4%29%2Ad+ left
2nd day:
They traveled +%281%2F2%29%2A%283%2F4%29%2Ad+, leaving +%281%2F2%29%2A%283%2F4%29%2Ad+
3rd day:
They traveled +%282%2F3%29%2A%281%2F2%29%2A%283%2F4%29%2Ad+ leaving +%281%2F3%29%2A%281%2F2%29%2A%283%2F4%29%2Ad+
4th day:
They traveled +%281%2F3%29%2A%281%2F2%29%2A%283%2F4%29%2Ad+
--------------------------------------
1st day:
+%281%2F4%29%2Ad+
2nd day:
+%281%2F2%29%2A%283%2F4%29%2Ad+=+%283%2F8%29%2Ad+
3rd day:
+%282%2F3%29%2A%281%2F2%29%2A%283%2F4%29%2Ad+=+%281%2F4%29%2Ad+
4th day:
+%281%2F3%29%2A%281%2F2%29%2A%283%2F4%29%2Ad+=+%281%2F8%29%2Ad+
They traveled the greatest distance on the 2nd day
-----------------
They traveled 12 km on the 3rd day
+%281%2F4%29%2Ad+=+12+
+d+=+48+
The whole trip was 48 km

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Using d as distance for the whole trip,
DAY Number___________Remaining Distance
1____________________%283%2F4%29d
2____________________%281%2F2%29%283%2F4%29d=highlight%28%283%2F8%29d%29
3____________________
4____________________0, trip done by end of day 4.

The first day and the third day, the same amount of distance was covered, one-fourth of d each of those days. Day 2 was the most distance covered. I figured through computing in my head, looking at the remaining distances for each day. Try this written if you need to.


The description also indicates, %281%2F8%29d=12.