Manyo Pak Mul...

Ikolah jawab nan sabana jawab, "instead of populun or ad verecundiam," bak 
kecek Sanak Ridha. Apolagi argumentum ad misericordiam.

Thanks you for the right answers, Brother Ridha.

Salam,
ZulTan, L, Bogor


Action cures fear.

-----Original Message-----
From: Ahmad Ridha <ahmad.ri...@gmail.com>
Sender: rantaunet@googlegroups.com
Date: Sun, 5 Aug 2012 10:57:47 
To: <rantaunet@googlegroups.com>
Reply-To: rantaunet@googlegroups.com
Subject: Re: [R@ntau-Net] OOT: Matematika 64 dan 65

2012/8/4 ZulTan <zul_...@yahoo.com>

> Assalamu'alaikum warahmatullaahi wabarakaatuhu,
>

Wa'alaykumus salaam warahmatullahi wabarakaatuh,


> Problem 1:
> A boat travels 12 km upstream and back in 1 hour 45 minutes.
> If the speed of the current is 3 km/h throughout, find the speed of the
> boat in still water, giving your answer correct to 3 significant figures.
>

s = 12 km
t = 1.75 h

12 / (v - 3) + 12 / (v + 3) = 1.75
(12(v+3) + 12(v-3))/(v^2 - 9) = 1.75
12(v+3) + 12(v-3) - 1.75(v^2 - 9) = 0
12v + 36 + 12v - 36 - 1.75v^2 + 15.75 = 0
- 1,75v^2 + 24v + 15,75 = 0

v = 14.342 km/h


> Problem 2:
> A motorist makes a journey of 240 km from Singapore to Malacca to visit
> his in-law at an average speed of X km/h. Write down an expression for the
> number of hours taken for the journey.
>

t1 = 240/X hour


> On his return jouney from Malacca to Singapore, his average speed is
> reduced by 6 km/h due to heavy traffic at the causeway. Write down an
> expression for the time taken for the return journey.
>

t2 = 240/(X - 6) hour



>  If the return journey takes 20 minutes longer, from an equation in X and
> solve it to find the average speed for each journey, giving your answer
> corret to two decimal places.
>

t2 = t1 + 1/3 hour

240/(X - 6) = 240/X + 1/3
720X - 4320 + X^2 - 6X - 720X = 0
X^2 - 6X - 4320 = 0

X = 68.80

X1 = X = 68.80
X2 = X - 6 = 62.80

Nice to have argumentation of mathematical nature, instead of ad populum
and ad verecundiam ones. Thank you, Pak ZulTan.

-- 
Abu 'Abdirrahman, Ahmad Ridha bin Zainal Arifin bin Muhammad Hamim
(l. 1400 H/1980 M)

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