VeritasPrepKarishma wrote:
Pansi wrote:
A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
(A) 2 hours, 225 miles
(B) 3 hours, 350 miles
(C) 4 hours, 450 miles
(D) 5 hours, 550 miles
(E) 6 hours, 650 miles
Using Ratios:
If Speeds are in the ratio 5:6, time taken will be in the ratio 6:5.
The difference of 1 is actually equal to 45 mins ie. 3/4 of an hour.So time taken in 1st case is 6*(3/4) = 4.5 hrs = 4 hrs 30 mins.
Since it is 30 mins late, it is scheduled to take 4 hrs for the journey.
Answer (C)
Responding to a pm:
Quote:
Just wanted to know what you mean by the highlighted part?
Check out these posts to understand ratio scale and multiplier concept:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... of-ratios/https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... os-in-tsd/We know that the time taken for the two speeds is in the ratio 6:5. This is a difference of 1 on the ratio scale between them (because 6-5 = 1)
But we know that in actual value terms, the difference between time taken for them is 30+15 = 45 mins. Say the actual time of arrival is 12 o clock. If it travels at 100 mph, it reaches at 12:30. If it travels at 120 mph, it reaches at 11:45. So the difference between the time taken in the two cases is 45 mins (which is 3/4 of an hour).
So the multiplier is 3/4 hr.
Time taken in first case = 6*(3/4)
Time taken in second case = 5*(3/4)