1. ## 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.

2. 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.

3. Hello, AHDDM!

You had a good start on #1 . . .

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 $\displaystyle 4\text{ km/hr.}$