# SOLUTION: Trains a and b are traveling in the same direction on parallel tracks. Train A is traveling at 80mph...? B is at 88mpr. Train A passes a station at 8:20pm. If train B passes the sa

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 Click here to see ALL problems on Quadratic Equations Question 214670: Trains a and b are traveling in the same direction on parallel tracks. Train A is traveling at 80mph...? B is at 88mpr. Train A passes a station at 8:20pm. If train B passes the same station at 8:50pm; at what time will train B catch up to train A?Found 2 solutions by Alan3354, Edwin McCravy:Answer by Alan3354(30993)   (Show Source): You can put this solution on YOUR website!Trains a and b are traveling in the same direction on parallel tracks. Train A is traveling at 80mph...? B is at 88mpr. Train A passes a station at 8:20pm. If train B passes the same station at 8:50pm; at what time will train B catch up to train A? --------------- Train A goes 40 miles in the 1/2 before train B passes the station. Train B is gaining on train A at 8 mph (88 - 80). 40/8 = 5 hours. 8:50 + 5 hours = 01:50 AM Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!Edwin's solution: Trains a and b are traveling in the same direction on parallel tracks. Train A is traveling at 80mph...? B is at 88mpr. Train A passes a station at 8:20pm. If train B passes the same station at 8:50pm; at what time will train B catch up to train ``` You can do it in your head: When train B passes the station at 8:50pm, train A has been travelingfor half an hour at 80mph (since 8:20pm) and so it is 40 miles from train B. So A's approach rate is 88-80 or 8mph and so it will take 5 hours to shrink A's 40 mile head start down to zero. So 5 hours from 8:50pm is 1:50am. (That is, provided the train did not cross over a time zone!) But your teacher doesn't want you to do it that way. That's too easy and you don't learn any algebra: Let t = the time train B travels till it catches A. Make this chart: Train Distance Rate Time A B Then fill in for the time of train A, since it traveled for half an hour (or .5 hours) past the station when B left the station. Also fill in their rates of 80mph and 88mph Train Distance Rate Time A 80 t+.5 B 88 t Now we use Distance = Rate x Time to fill in the distances both will have traveled from the station. Train Distance Rate Time A 80(t+.5) 80 t+.5 B 88t 88 t When B catches up to A they will have traveled the same distance so we set those two distances equal: A's distance from station = B's distance from station 90(t+.5) = 88t Solve that and get t=5 hours Then 5 hourslater than 8:50pm is 1:50am, provided no time zone was crossed. Edwin```