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OG question 134 - estimated avg speed

This topic has 2 expert replies and 1 member reply
NadineKh Newbie | Next Rank: 10 Posts Default Avatar
Joined
28 Jul 2017
Posted:
5 messages

OG question 134 - estimated avg speed

Post Tue Aug 15, 2017 1:00 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    In planning for a car trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?
    (1) Joan’s estimate for the distance was within 5 miles of the actual distance.
    (2) Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.

    Answer: E

    How would you rephrase the problem and how would you solve it?
    I'm trying to find a more systematic way to solve this type of problem than trying numbers.

    Thank you!

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    Post Tue Aug 15, 2017 9:38 am
    NadineKh wrote:
    In planning for a car trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?
    (1) Joan’s estimate for the distance was within 5 miles of the actual distance.
    (2) Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.

    Answer: E

    How would you rephrase the problem and how would you solve it?
    I'm trying to find a more systematic way to solve this type of problem than trying numbers.

    Thank you!
    Well, I'm not sure I'd bother rephrasing this one. Here's how I think about it: you can dismiss each statement on its own almost immediately. The first statement tells you nothing about speed and the second tells you nothing about distance.

    Together, we want to see if we can get a YES and a No to the original question. Well, we can obviously get a YES - it's possible that Joan estimated the distance and the speed with uncanny precision, getting both on the nose, and so she'd have gotten the time on the nose as well. So in this case, YES, her estimate would be within .5 hours of the actual time.

    So all we need is a NO.
    Actual distance = 5
    Joan's estimate = 10

    Actual speed = 20mph
    Joan's estimate = 10mph

    Actual Time = 5/20 = .25 hours
    Joan's estimate = 10/10 = 1 hour
    1 - .25 = .75, so NO, her estimate is not within .5 hours. Together the statements are not sufficient. The answer is E

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    Post Tue Aug 15, 2017 10:00 am
    Come to think of it, we don't have to think about this one very hard.

    Together:
    Scenario 1: She gets the distance and the rate exactly right - YES, she's within 5. hours of the actual time.

    Scenario 2: actual rate = 0; estimated rate = 10. Clearly, NO, she's not within .5 hours of the actual time, no matter the distance. She's not moving.

    Answer is E

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    NadineKh Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    28 Jul 2017
    Posted:
    5 messages
    Post Tue Aug 15, 2017 10:19 am
    Thank you very much!!

    It also helped me interpreting it more intuitively: since we have delta (differences between estimation and reality) in both numerator and denominator, we can't have an idea of the % deviation without knowing the value of the ratio.

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