# Simplifying Rational Expressions / Distance (Word) Problems

• Oct 15th 2008, 05:20 PM
RAWKETchild
Simplifying Rational Expressions / Distance (Word) Problems
Hi, I need help on trying to solve these two equations:

"Express in simplest equivalent form."

http://img225.imageshack.us/img225/4...e15855bsn8.jpg

and

http://img266.imageshack.us/img266/3...e15855ezh6.jpg

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!
• Oct 15th 2008, 05:56 PM
skeeter
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

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

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

$st = 300$

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

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

3. let s = kyle's speed

(time)(speed) = distance

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

solve for s