急 ! F5 about equations 1條

Let
T1 = Hours Frank needs to complete the job alone = t
T2 = Hours Peter needs to do the same thing alone = t + 1

Speed of Frank to paint alone = V1
(unit: a flat of walls painted per hour ... or job done / hour :D )
Speed of Peter to paint alone = V2

i.e.
V1 = 1/T1 = 1/t
V2 =1/T2 = 1/(t + 1)

Now, they paint it together in 6 hours:
(Speed of Frank + Speed of Peter) x 6 (hours) = 1 job done
6(V1 + V2) = 1
6[1/t + 1/(t + 1)] = 1
6[(t + 1) + t]/t(t + 1) = 1
6(2t + 1) = t(t + 1)
t^2 - 11t - 6 = 0

t
= {11 +/- [(-11)^2 - 4(-6)]^(1/2)}/2
= [11 +/- (145)^(1/2)] / 2
= [11 + (145)^(1/2)] / 2 or [11 - (145)^(1/2)] / 2 (rejected)
= [11 + (145)^(1/2)] / 2

i.e. Frank needs [11 + (145)^(1/2)]/2 hours to complete the job alone.
(Approximately 11.52 hours :D)

Let Frank takes x hours to finish and Peter takes (x+1) hours to finish.
x+(x+1) = 6

got it?