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 ?

Rating

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：

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• 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 &lt;----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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