F.4 Quadratic Equations

1.A man walked 12km at a certain rate, and than 6km further at a rate 1/2km faster. He would have saved 20 minutes if he completed the whole journey at the faster rate.

(a) What was his rate in the first 12km ?

(b) How long would it take him to complete the whole journey if he kept walking at the slower rate ?

2 Answers

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  • 1 decade ago
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    1.A man walked 12km at a certain rate, and than 6km further at a rate 1/2km faster. He would have saved 20 minutes if he completed the whole journey at the faster rate.

    (a) What was his rate in the first 12km ?

    rate = v

    12/v + 6/(v+1/2) = 18/(v+1/2) + 20

    12/v = 12/(v+1/2) + 20

    12(v+1/2) = 12v + 20v(v+1/2)

    12v + 6 = 12v + 20v^2 + 10v

    20v^2 + 10v - 6 = 0

    10v^2 + 5v - 3 = 0

    v = [ -5 + sqrt(145) ] / 20 = 0.3521 km/min

    (b) How long would it take him to complete the whole journey if he kept walking at the slower rate ?

    18/v = 51.1248 min.

    2007-10-26 01:16:09 補充:

    上面位係咪計錯數...投我一票, 唔該

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  • 1 decade ago

    a) let x km/min be the rate for the first 12km

    因為頭12km 用x km/min, 之後6km 用 (x + 1/2) km/min

    所以total 時間

    t = [12 / x] + [6 / (x + 1/2)]

    如果全程用 (x + 1/2) km/min去行

    total 時間

    = 18 / (x + 1/2) = t - 20 <----少20min

    所以 t = 18 / (x + 1/2) + 20 = [12 / x] + [6 / (x + 1/2)]

    x = 0.2

    rate in first 12km = 0.2 km / min

    b) if he use 0.2km / min for whole journey,

    18(km) / 0.2 (km/min) = 90min = 1.5h

    Source(s): me
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