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Algebra - Rational Equations

1. The speed of train A is 10 mph slower than the speed of train B. Train A travels 230 miles in the same time it takes train B to travel 280 miles. Find the speed of each train.
2. The Office Jet printer can copy Maria's dissertation in 8 min. The Laser Jet printer can copy the same documents in 22 min. If the two machines work together, how long would they take to copy the dissertation?
3. Simplify by removing factors of 1
4. To determine the number of deer in a game preserve, a conservationist catches 408 deer, tags them and lets them loose. Later, 576 deer are caught; 192 of them are tagged. How many deer are in the preserve?
5. Find all numbers for which the rational expression is undefined.
6. Add. Simplify if possible
7. Simplify by removing factors of 1
8. Multiply and simplify
9. Simplify by removing factors of 1
10. Solve.

[See the attached questions file.]

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1. The speed of train A is 10 mph slower than the speed of train B. Train A travels 230 miles in the same time it takes train B to travel 280 miles. Find the speed of each train.

Let the speed of B be x miph. Then the speed of A is x - 10 miph.
Time of travel for train A = distance/speed = 230/(x- 10)
Time of travel for B = 280/x
By data, 230/(x - 10) = 280/x
230x = 280(x - 10)
230x = 280x - 2800
50x = 2800
x = 2800/50 = 56 miph (Train B) and 56 - 10 = 46 miph (Train A).

2. The Office ...

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