Anu26 wrote:
Bunuel wrote:
carcass wrote:
Train A traveling at 60 m/hr leaves New York for Dallas at 6 P.M. Train B traveling at 90 m/hr also leaves New York for Dallas at 9 P.M. Train C leaves Dallas for New York at 9 P.M. If all three trains meet at the same time between New York and Dallas, what is the speed of Train C if the distance between Dallas and New York is 1260 miles?
A. 60 m/hr
B. 90 m/hr
C. 120 m/hr
D. 135 m/hr
E. 180 m/hr
Relative speed of train A and train B is 90-60=30 miles per hour, thus B will gain 30 miles every hour compared to A.
Now, in 3 hours (from 6 P.M. to 9 P.M.) that A traveled alone, it covered 60*3=180 miles. To catch up A (to meet A), B will need 180/30=6 hours.
Next, in 6 hours B will cover 6*90=540 miles to the meeting point, thus C covered 1260-540=720 miles.
Since C also needed 6 hours to meet A and B (C also left at 9 P.M), then its rate is 720/6=120 miles per hour.
Answer: C.
Hope it's clear.
Can you please explain : To catch up A (to meet A), B will need 180/30=6 hours
We can calculate the solution in this manner too. Lets say Train A starts at 6pm at 60miles/hr and train B at 90miles/hr.
Now by 9 pm train A would have travelled 180 miles.
lets say train A and train B meet after x hours after 9 pm hence if we equate the distance traveled by two train in X hours after 9 PM it will be:
60(x+3) = 90x (x+3 for train because of time from 6pm to 9 pm)
solving above equation we get x = 6 hours
So the distance traveled in 6 hours by train B is 90 * 6 = 540 miles/hour
Question says train C also meets train A and B at same time. So distance traveled by train C is 1260 - 540 = 720 miles.
Again we are told train C started at 9 pm. So hours traveled by train C before meeting train A and B is 6 hours.
So speed of train C = 720/6 = 120 miles/hour
Please give kudos if you like the explaination