GMAT Question of the Day - Problem Solving - Rate
From her home, Daria traveled east for 2.6 miles and for every 15 minutes she traveled 1 mile. At some point she returned home on the same path. If after the initial 2.6 miles Daria traveled for 45 minutes and if for the entire journey she took no breaks then for how many miles did she travel west?
GMAT Question of the Day Solution
GMAT Rate questions can be organized in T's. If you've been doing GMAT question of the day for a while you can probably skip some of this or stick around for a refresher. A rate T is great because it shows all of the iterations of the old Distance = Rate * Time formula. It is also very compact and that economy is nice when you have a limited amount of erasable pad space. In this question we know Daria's rate, a portion of the distance that she traveled east and the portion of the time that she traveled after that initial distance. This is the time to think about what you want to do. Take a second to plan. How do these pieces of information work together? The important thing to come away with is that for every mile she travels east she will have to travel west. So the 45 minutes have to take that into account. Also - she will have to travel back the 2.6 miles that she has already gone. Let's try to calculate how far Daria can go in the 45 minutes. Then we can take that result and add it to the initial 2.6 miles and we'll have the distance traveled west.
So the distance part of the T should be the 2.6 miles that we have to travel back plus 2 times the miles that we will travel (to count the fact that any mile east must also be traveled west). The rate is 1/5 and the time is 45 minutes. Take that result (.2) and add it to 2.6.