hellosanthosh2k2 wrote:
niks18 wrote:
hellosanthosh2k2 wrote:
Hi
niks18,
Thanks for reply.
https://gmatclub.com/forum/stations-x-a ... 00088.htmlThis is the question, I was mentioning. In the link question, statement 2 is not sufficient, can we apply the same logic for this question.
Posted from my mobile deviceHi
hellosanthosh2k2There is a basic difference between two questions.
In this question, we can use average speed because when the two meet then relatively they have traversed the entire distance. and we only need to know the distance covered till that point.
In the other question, trains meet and then the trains continue to run till they reach their destination. So you can use average speed concept only till the point they meet, post that to know the time taken to reach their destination you will have to know their individual speeds for the remaining distance. the average speed of both train P & Q is not mentioned in statement 2 when they meet.
let us assume the average speed of train P was a and that of train Q was y when they crossed each other, so you will have 2a+2b=250 =>a+b=125. Now we don't know what is a or b here. So the statement 2 is insufficient
Hi
niks18I was trying to prove Statement 1 as not sufficient with two cases
Say
average speed of Bill = 300 ft/hr (1.5 times Sally's as mentioned in statement 1), Sally = 200 ft/hrCase 1:
Until the point they meet, Let average speed of
Bill = 100ft/hr, Sally = 400 ft/hrso time to meet = 500/(100+400) = 1 hr
so they meet at 100ft distance from where Bill start.
After meet, say average speed of Bill is B for remaining distance of 400 ft,
then 500/(1 + (400/B)) = 300 (his overall average speed), solving we get B = 600ft/hr, so after meet, Bill speeds up to 600 ft/hr
Similarly after meet, say average speed of Sally S for remaining distance of 100ft,
then 500/(1 + 100/S) = 200 (her overall average speed), solving we get S = 100/1.5 ft/hr, So after meet, Sally slows down to 100/1.5 ft/hr
so in this case, Bill average speed = 300 ft/hr and Sally average speed = 200 ft/hr, but they meet at 100 ft from where Bill started.
Case 2:
Bill and Sally travel at same constant speed of 300 ft/hr and 200 ft/hr respectively, in this case, they meet at 300 ft from where Bill started.
So two cases, different point of meet. I think unless and until the statement says, Bill and Sally ran at constant speed, statement 1 won't be sufficient. Am i missing anything?
Thanks
Hi
hellosanthosh2k2For this question which is Case 1, you have considered one average speed and then again considered a different average speed. Representing the question again here for clarity -
Quote:
Bill and Sally see each other across a field. They are 500 feet apart. If at the same instant of time they start running toward each other in a direct line how far will Bill have traveled when they meet?
(1) Bill ran at an average speed that was 50% greater than Sally's average speed.
(2) Bill ran at an average speed 4 feet per second faster than Sally's average speed.
here when Bill & Sally meet, then their average speed hold the relation of 1.5:1. This average is in totality till they meet. So let the two meet at point P
Bill______________P(Bill meets Sally)___________Sally. Bill's average speed till P is x & Sally's average speed till P is y, so we have x=1.5y. Within this average speed we are not going to again assume some different average speed.
And for the second question
Quote:
Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.
We know XY=250 X_____________Y. Let the trains meet at point A i.e X___________A_______Y
Average speed of train P till point A=70 and time taken 2 hours. So distance XA=70*2=140
we know XY=250, so AY=XY-XA=250-140=110
so train Q traveled 110 Km. Now train P has to reach Y which and train Q has to reach X, so you can see which train is closer to its destination AT THE TIME WHEN THEY PASSED each other.
So in both these cases Statement 1 is sufficient.