Problem Solving

swerve wrote:Train A and B, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train A left at 4 pm traveling at a speed of 60 miles per hour, and train B left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?

A. 7:20 pm
B. 8:55 pm
C. 9:05 pm
D. 9:20 pm
E. 9:25 pm

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.

If train A travels for t hours at 60 mph, it will cover 60t miles.
If train B leaves 1 hour 45 min, or 1 3/4 = 7/4 hours after train A, then it will travel for 7/4 hours less than A does, or t - 7/4. If B travels at 45 mph for t -7/4 hours, it will cover 45(t - 7/4) miles
Together they cover 455 miles, so 60t + 45(t - 7/4) = 455.
60t + 45t - 45 *(7/4) = 455
105t = 455 + 45 *(7/4) ---> multiply through by 4 to get:
420t = 1820 + 45 * 7
420t = 1820 + 315
420t = 2135 ---> divide numerator and denominator by 7 to get:
60t = 305
t = 305/60 = 5 + 5/60, or 5 hours and 5 minutes. 5 hours and 5 minutes after 4 pm would be 9:05PM. The answer is C