John B.
asked • 07/17/23Math Question Related to Algebra
Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and train B is traveling at 70 mph. Train A passes a station at 12:20 P.M. If train B passes the same station at 12:32 P.M, at what time will train B catch up to train A?
My question is why add 12 minutes to A and not B when putting together an equation?
More
2 Answers By Expert Tutors
Bradford T. answered • 07/18/23
Tutor
4.9
(29)
Retired Engineer / Upper level math instructor
The is a distance=rate×time problem.
You want to make the distances traveled by both trains starting at 12:32 PM the same. In the 12 minutes since 12:20, train A has traveled 60×12/60 = 12 miles. (Keeping everything in minutes)
DistanceA=DistanceB
12 + 60t/60 = 70t/60
720 +60t = 70t
t = 720/10 = 72 minutes = 1:12
12:32+1:12 = 13:44 = 1:44 PM
We know that Train B is 12 minutes behind (0.2 hrs) when Train A passes the station, but is 10 mph faster than Train A.
When Train A passes the station, the distance between Train B and Train A would be 70*0.2 = 14 miles
This means that the time it will take for Train B to catch up to Train A is 14mi/10mph = 1.4 hrs
Adding 1.4 hrs to 12:20pm, which is 1hr and 24 minutes, will be 1:44pm.
Hope this helped!
John B.
Thank you, my one last thing is why would you multiply 0.2 by 70? What’s the logic?
Report
07/18/23
AJ L.
tutor
The time Train B is behind Train A when Train A passes the station, 0.2 hours, times Train B's speed of 70mph, helps determine the distance Train B is away from Train A at that moment.
Report
07/18/23
AJ L.
tutor
If you need more help, I suggest scheduling a time and we can go over problems like this together!
Report
07/18/23
John B.
Wouldn’t 1.4 hours be the time it takes B to catch A? Wouldn’t you add 1.4 to B then?
Report
07/19/23
AJ L.
tutor
For your first question, yes. However, keep in mind that A has already passed the station before B did, so you'd need to add on the time it takes to A to travel past the station plus B's time to get to the station after A does.
Report
07/19/23
AJ L.
tutor
Bradford T.'s answer also works
Report
07/19/23
John B.
👍
Report
07/19/23
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
John B.
And if you could explain in detail how to actually solve it that would be great07/18/23