SOLUTION: Trains A and B are traveling in the same direction on parallel lines. Train A is traveling at 100 miles per hour and Train B is traveling 125 miles an hour. Than Train A passes a s

Algebra ->  Finance -> SOLUTION: Trains A and B are traveling in the same direction on parallel lines. Train A is traveling at 100 miles per hour and Train B is traveling 125 miles an hour. Than Train A passes a s      Log On


   

Question 473924: Trains A and B are traveling in the same direction on parallel lines. Train A is traveling at 100 miles per hour and Train B is traveling 125 miles an hour. Than Train A passes a station at 10:25 AM. If Train B passes the same station at 10:37 AM. What time will B catch up with Train A? When will Train B catch up with Train A?
When will Train B catch up to Train A?
Time ??? PM or AM?
Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Train A has a head start of how many miles when
train B passes the station?
10:37 - 10:25 = 12 minutes
Train A's head start is:
+d%5B1%5D+=+100%2A%2812%2F60%29+
+d%5B1%5D+=+20+ mi
-------------------
Now start a stopwatch when B passes the station.
Both trains will travel for the same amount of time, t
until they meet.
-------------------
Let +d+ = the distance that B has to go until they meet
Then +d+-+20+ = the distance that A has to go until they meet
-------------------
For B:
(1) +d+=+125t+
For A:
(2) +d+-+20+=+100t+
--------------------
Substitute (1) into (2)
+125t+-+20+=+100t+
+25t+=+20+
+t+=+20%2F25+
+t+=+4%2F5+ hrs
They will meet in +4%2F5+ hrs or +%284%2F5%29%2A60+=+48+ minutes
after B leaves station
10:37 AM + 48 min = 11:25 AM is the time
B passes A
---------------
check answer:
A's distance from station is d
A's time from station is +12%2F60+%2B+4%2F5+=+1+ hr
+d+=+100%2A1+
+d+=+100+ mi
B's distance from station is also d
+d+=+125%2A%284%2F5%29+
+d+=+100+ mi
OK