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Rates and Distance

This topic has 2 expert replies and 0 member replies
singhmaharaj Senior | Next Rank: 100 Posts
Joined
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Posted:
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Target GMAT Score:
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Rates and Distance

Post Tue May 06, 2014 5:17 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?


    A) 6 2/3

    B) 15

    C) 20

    D) 25

    E) 26 2/3

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    Post Tue May 06, 2014 5:20 am
    singhmaharaj wrote:
    A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?


    A) 6 2/3

    B) 15

    C) 20

    D) 25

    E) 26 2/3
    Here's one approach:

    5 minutes after the cyclist passes the hiker
    The cyclist is traveling 16 mile per hour faster than the hiker.
    Distance = (time)(speed)
    Time = 5 minutes = 1/12 hours
    So, the distance between them = (16)(1/12) = 16/12 = 4/3 miles

    Time for hiker to catch up
    Distance = 4/3 miles
    Hiker's speed = 4 miles per hour
    Time = distance/time = (4/3)/4 = 1/3 hours = 20 minutes = C

    Cheers,
    Brent

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    Post Tue May 06, 2014 5:28 am
    Quote:
    A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continue to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?

    1.6 2/3
    2.15
    3.20
    4.25
    5.26 2/3
    Rate and time are RECIPROCALS.
    The RATE RATIO = hiker : cyclist = 4:20 = 1:5.
    Thus, the TIME RATIO = hiker : cyclist = 5:1.
    The implication is that the hiker will take 5 TIMES AS LONG as the cyclist to travel the same distance.
    Thus, when the cyclist passes the hiker, the hiker will then require 25 minutes to travel the number of miles traveled by the cyclist in 5 minutes.
    Time difference = hiker's time - cyclist's time = 25-5 = 20 minutes.
    Thus, the cyclist will have to wait 20 minutes for the hiker to catch up.

    The correct answer is C.

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