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M3
Lv 7
M3 a posé la question dans Science & MathematicsMathematics · il y a 8 ans

Weekend Speed-Time Puzzle 2?

Car A begins to drive from the town to the airport at 9.00 am at x km/hr

Car B begins to drive from the airport to the town at 9.17 am at y km/hr

After they pass each other, car A takes 10 minutes to reach the airport, while car B takes 20 minutes to reach the town.

the question is: At what time do the cars pass each other ?

note:

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This isn't a difficult problem, BA will be given to the SIMPLEST correct solution.

Mise à jour:

.

@Julius N

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10 minutes is "after they pass each other"

Mise à jour 2:

.

@Julius N

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10 minutes is "after they pass each other"

Mise à jour 3:

.

since both answers are good, TU's to both & BA to 1st in.

2 réponses

Pertinence
  • J
    Lv 6
    il y a 8 ans
    Réponse favorite

    if T = time for A for the distance town-airport

    elapsed time to meet B = T-10

    T-10 = 17 + T'-20

    T = T'+7

    with T' = time for B for the distance airport-town

    10x + 20y = D

    with D = distance town-airport

    x = D/T | y = D/T'

    20D/T' + 10D/T = D

    20/T' + 10/T = 1

    20/T' + 10/(T'+7) = 1

    ==>T' = 28 and T = 35

    T-10 = 25 minutes

    at time : 9:25 am ..........answer

    ++++++++++++++++++++++++++++++++++++++

  • il y a 8 ans

    if car A leaves town at 9:00 am and it takes it 10 minutes to get to the airport then it will be at the airport at 9:10.

    since car B doesn't leave the airport until 9:17, they won't really be passing each other.

    They will be sitting next to each other from 9:10 , when car A arrives, until 9:17 when car B leaves.

    oops, thank you M3 for pointing that out. My students do it all the time - they misread a problem and solve the problem they read instead of the one I made up.

    OK, let's do it again. The distance traveled in time t by A equals the distance traveled in 20 minutes by B.

    also, the distance traveled by A in 10 minutes equals the distance traveled by B in t-17 minutes.

    so xt = 20y and 10x = (t-17)y

    so x = 20y/t and x = (t-17)y/10

    so 20/t = (t-17)/10

    so 200 = t2 - 17t

    and t = 25

    so they meet at 9:25

    never mind, I see J already got the answer.

    Julius

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