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Algebra questions

1. A passenger train leaves the train depot 2 hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in three hours.

2. Solve

3. How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?

4. Solve using quadratic formula.

5. Tickets to McClymonds High school Concert, featuring Destiny's Child Cost $11.00 for students and $4.00 for faculty. On Tuesday 36 tickets were sold for a total of $214.00. How many tickets of each kind were sold?

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The solution file is attached and also I have pasted answers here.

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A passenger train leaves the train depot 2 hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in three hours.

Solution:
At the point where the passenger train over takes the freight train, the distance covered by both the trains are the same.

Let d be the distance covered by the trains.
The passenger train overtakes the freight train in three hours. So time taken by passenger train is 3 hours and time taken by freight train is 5 hours (because freight train leaves the dept 2 hours before the passenger train).

We have to find the rate of each train.

Let x be the speed of the passenger train. Then speed of the freight train would be x-20 mph (because the freight train is traveling 20 mph slower than the passenger train).

For passenger train:
Distance = d, ...

Solution Summary

There are several problems here, covering intersection of freight trains, equations with square roots, quadratic equations, a mixture problem, and determining number of tickets sold.

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