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Time rate and distance

This topic has 3 expert replies and 1 member reply
Time rate and distance Post Wed Mar 11, 2015 1:10 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The question had me stumped because i forgot which formula i had to use, either d*r/t or r*d/t.

    The question is as follows:

    Train A left Centerville Station, heading toward Dale City Station at 3:00pm. Train B left Dale City Station heading toward Centerville Station at 3:20pm. on the same day. The trains rode on straight tracks that were parallel to each other. If train A traveled at a constant speed of 30 miles per hour, Train B traveled at a constant rate of 10 miles per hour, and the distance between Centerville Station and Dale City station is 90 miles, when did the trains pass each other?

    A.)4:45pm
    B.)5:00pm
    C.)5:20pm
    D.)5:35pm
    E.)6:00pm

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    Post Wed Mar 11, 2015 1:22 pm
    datonman wrote:
    Train A left Centerville Station, heading toward Dale City Station at 3:00pm. Train B left Dale City Station heading toward Centerville Station at 3:20pm. on the same day. The trains rode on straight tracks that were parallel to each other. If train A traveled at a constant speed of 30 miles per hour, Train B traveled at a constant rate of 10 miles per hour, and the distance between Centerville Station and Dale City station is 90 miles, when did the trains pass each other?

    A.)4:45pm
    B.)5:00pm
    C.)5:20pm
    D.)5:35pm
    E.)6:00pm
    3:00pm - Train A (traveling 30 miles per hour) left Centerville Station, heading toward Dale City Station
    If the train travels 30 miles every HOUR, then it travels 10 miles every 20 minutes.
    In other words, at 3:20pm, Train A has already traveled 10 miles.
    So, at 3:20, the trains are now 80 miles apart.

    3:20pm - Train B (traveling 10 miles per hour) left Dale City Station heading toward Centerville Station
    At this point (at 3:20pm), the trains are 80 miles apart.
    Also, every hour, Train A moves 30 miles toward train B, and Train B moves 10 miles towards train A. This means the gap between them is decreasing at a rate of 40 miles per hour.

    At this rate, the 80-mile gap will be reduced to zero miles (i.e., the trains meet) in 2 hours.

    So, the trains will meet at 3:20pm + 2 hours = 5:20pm
    Answer: C

    Cheers,
    Brent

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    Post Wed Mar 11, 2015 3:56 pm
    Hi datonman,

    Brent's solution is spot-on, so I won't rehash any of that here. Instead, I want to point out a few aspects of these types of questions:

    1) The Distance Formula is Distance = (Rate)(Time). However you choose to 'manipulate' it, THAT is the formula.

    2) This prompt is an example of a Combined Rate question. These types of questions are relatively rare on Test Day (you'll likely see just one) and they're almost always 'story problems.' As such, they take longer than average to solve and are worth less than most other categories to your overall score.

    3) The key to dealing with these types of prompts involves figuring out what happens when both 'entities' (trains, cars, people, etc.) are moving at the same time. If one entity moves for a certain amount of time before the other gets moving, then you have to deal with that part of the 'math' first.

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    Rich

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    Thanked by: umasarath52
    Post Tue Mar 17, 2015 3:15 am
    Brent's method is probably the fastest way to approach this question. Alternatively, you can plug and chug in a R*T = D chart. If we know that A left 20 minutes earlier, then it traveled for 1/3 of an hour longer than B did. Call their times 't + 1/3' and 't' respectively. Our chart will look like this:




    Now simply solve the distance column to get the following equation: 30t + 10 + 10t = 90
    40t = 80
    t = 2

    If they pass once train B has been traveling for 2 hours, it will be 5:20

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    Post Sun Mar 22, 2015 10:58 pm
    DavidG@VeritasPrep wrote:
    Brent's method is probably the fastest way to approach this question. Alternatively, you can plug and chug in a R*T = D chart.
    This is a great method to remember. If you forget the formula, you can almost always still solve this problem anywhere if you just plot the trains - and you can often approximate with the answers to save time.

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