# Word Problems

• Dec 20th 2007, 10:31 AM
AHDDM
Word Problems
Bah its always these I get stuck on.

1. A man walks 18km he goes .5km/h faster than planed and reaches destination 30mins early. What was his planned speed.

2. Chess tournament as 45 games everyone plays together once. How many players attend.

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For number one I used these equations but couldnt come out with anything
18=xt
18=(x+0.5)(t-0.5)

And for number two I got 10 people which is right answer but I did with arithmetic and my teacher wants algebra.
• Dec 20th 2007, 10:56 AM
Plato
Quote:

Originally Posted by AHDDM
2. Chess tournament as 45 games everyone plays together once. How many players attend.

And for number two I got 10 people which is right answer but I did with arithmetic and my teacher wants algebra.

Use combinations.
$\displaystyle _n C_2 = {n \choose 2} = \frac{{n(n - 1)}}{{2 \cdot 1}} = 45$

Solve for n.
• Dec 20th 2007, 11:31 AM
Soroban
Hello, AHDDM!

You had a good start on #1 . . .

Quote:

1. A man walks 18 km.
If he goes 0.5 km/h faster than planned, he reaches his destination 30 mins early.
What was his planned speed.

This is the way I baby-talk my way through these problems . . .

We know: .$\displaystyle \text{Distance} \:=\:\text{Speed} \times \text{Time} \quad\Rightarrow\quad T \:=\:\frac{D}{S}$

Let $\displaystyle x$ = his planned (original) speed ... in km/hr.

Walking $\displaystyle 18$ km at $\displaystyle x$ km/hr, it takes him: .$\displaystyle \frac{18}{x}$ hours.

If he walks at $\displaystyle x + 0.5$ km/hr, it takes him: .$\displaystyle \frac{18}{x+0.5}$ hours.

. . And this faster time is 30 minutes less than his planned speed: .$\displaystyle 0.5 \text{ hour.}$

There is our equation! . . . . .$\displaystyle \frac{18}{x+0.5} \;=\;\frac{18}{x} - 0.5$

Multiply through by $\displaystyle x(x+0.5)$

. . $\displaystyle 18x \:=\:18(x+0.5) - 0.5x(x + 0.5) \quad\Rightarrow\quad 0.5x^2 + 0.25x - 9 \:=\:0$

Multiply by 4: .$\displaystyle 2x^2 + x - 36 \:=\:0$

. . which factors: .$\displaystyle (x - 4)(2x + 9) \:=\:0$

. . and has the positive root: .$\displaystyle x \:=\:4$

Therefore, his planned speed was $\displaystyle 4\text{ km/hr.}$