# Thread: Simplifying Rational Expressions / Distance (Word) Problems

1. ## Simplifying Rational Expressions / Distance (Word) Problems

Hi, I need help on trying to solve these two equations:

"Express in simplest equivalent form."

and

Now for the word problems... I'm having trouble with these distance problems since I don't know where to place which numbers... so it'd be great if someone could show me each step and explain why the numbers are there... I'd appreciate it. =)

"A plane takes the same amount of time to fly 1500 km at 100 km/h below its top speed as it takes to fly 1250 km at 200 km/h below its top speed. What is the plane's top speed, in kilometers per hour?"

"David flew 300 km on a commuter plane, then 2000 km on a passenger jet. The passenger jet flew twice as fast as the commuter plane. The total flying time for the journey was 3 1/4 hours. What was the speed of each plane in kilometers per hour?"

"Nadia and Kyle shared the driving on a 1250 km trip from Edmonton to Vancouver. Nadia drove for 6 hours and Kyle drove for 8 hours. Nadia drove 10 km/h faster than Kyle. How fast did Kyle drive?"

Thanks, any help is appreciated!

2. for the two rational expressions ... try factoring the numerators and denominators, then see what common factors will divide out.

1. time = (distance)/(speed)

let s = the plane's top speed

$\displaystyle \frac{1500}{s - 100} = \frac{1250}{s - 200}$

solve for s.

2. (speed)(time) = distance

let s = speed of the commuter plane
2s = speed of the jet
t = time for the commuter plane
3.25 - t = time for the jet

$\displaystyle st = 300$

$\displaystyle 2s(3.25 - t) = 2000$
$\displaystyle 6.5s - 2st = 2000$

you should be able to substitute 300 for $\displaystyle st$ in the second equation ... solve for s.

3. let s = kyle's speed

(time)(speed) = distance

$\displaystyle 8s + 6(s+10) = 1250$

solve for s