john1234 wrote:During a 40 mile trip, Marla traveled at a average spped of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for the last 40-y miles of the trip.The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she had traveled at an average speed of x mile per hour for the entire trip?
1) x = 48
2) y = 20
It took me 3 minutes to solve this question.I need any help i can get on this.Ian and Stuart pls help.
An interesting question. The first observation I'd make: it's absolutely clear that you could answer the question with both statements, since then you'd know all of the numbers. That should certainly make you suspicious that one statement is actually sufficient alone. 1) is not enough, because we have no idea what y is, and y is clearly important here. If you see that, you're down to B and C as answer choices, and you could guess B and be correct most of the time (at least on more difficult questions), since C is 'too obvious'.
Still, I don't like guessing, so let's see why 2) is sufficient. You can certainly see this algebraically, but that isn't actually necessary. The numbers in the question confuse matters a bit, but the essential idea is this:
If it would take you t hours to travel d miles at speed s, then over d miles,
-if you travel at speed 2s, it will take t/2 hours (if you double your speed, you'll cut your time in half);
-if you travel at speed 3s, it will take t/3 hours (if you triple your speed, you divide your time by 3)
-if you travel at speed 1.25s = 5s/4, as in the question, your time will be 4t/5.
You can see this by plugging into the t = d/s equation.
So we know that for part of the trip, the part at 1.25x miles per hour, the time was 4/5ths of what it would have been had the speed simply been x. We only need to know for what fraction of the trip the time was reduced by this ratio- and Statement 2 tells us that the time was reduced for exactly half of the trip. So sufficient.
If you want the actual answer- say it would have taken t hours at speed x. The first half would normally take t/2 hours, but at speed 1.25x, it will take 4/5ths as long - 2t/5 hours. The second half, at speed x, takes t/2 hours. So if half the trip is completed at speed 1.25x, the other half at speed x, the time will be:
2t/5 + t/2 = 9t/10
At the given speeds, the total time will be 90% of what it would have been at speed x the entire trip.
