StaceyKoprince Wrote:If they both leave at the same time, the one that has been traveling faster up to that point in time will be nearer to its destination. Note that the faster one could slow down considerably afterwards - but I don't care about that or about when they actually reach their destinations. I only care about where they are when they pass.
First, sketch this out on paper.
(1) At the time they pass, they've been going for 2 hours. If P has averaged 70mph to that point, then P has gone 140 miles. The tracks are 250 miles long, so P still has 110 miles to go. At this "passing" point, Q has then gone 110 miles and still has 140 miles to go. So P is closer to its destination. Sufficient.
(2) Q averaged 55mph for the whole trip. I'll try to see if I can both make Q the "closer" train and P the "closer" train with this info. To average 55mph over 250 miles, the train has to run about 4.5 hours (because 250/4.5 is just about 55).
First, let's say Q goes 10mph for the first 2 hours and then some really fast speed after that to up the overall average to 55mph. (Note: it'd have to approach 450+ mph, but the problem doesn't tell us there's a max speed the train can travel!) After 2 hours, Q has gone 20 miles and P has gone 230 miles. P is closer to its destination.
Now let's say Q goes 100mph for the first 2 hours and then some really slow speed after that to bring the overall average down to 55mph. After 2 hours, Q has gone 200 miles and P has gone 50 miles. Q is closer to its destination.
I can't say one is definitely closer than the other. Insufficient. Answer is A.
I have two questions regarding this question
1) At the time when the two trains passed, train P had averaged a speed of 70 miles
per hour.
In above statement, average speed is improper word ,don't you think.?
Because if you define speed at particular point,then it is called instantaneous speed
So average speed of 70 miles per hour is confusing
2)why can't we use below method to find the speed of train P ?
Rp + Rq = distance /time=250/2
Where, Rp= speed of train P
Rq= speed of train Q = 55 mph
I really appreciate any help you can provide