Expert: Richard J. Raridon - 6/11/2006

Question
I need help on these following problems, I need to know to do the set-up and the first few steps would be great, the rest I can do. Your help is greatly appreciated and I thank you for your time.


1.Marsha must mow the lawn before she can go swimming. She realizes that it would take her 50 minutes to do it by herself. So she gets Fran to help her. The job is completed in 30 minutes. How long would it have taken Fran to do the job alone?

2. A torrential rain can fill the basin behind a flood control dam in  5 hours. With the dam's floodgates open, a full basin wil drain in 20 hours. How long would it take to fill the basin in a torrential rain with the floodgates open?

3. Cora Spondence can stuff a pile of letters into envelopes in 3 hours. N.V. Lopes takes 4 hours to do the same job. How many hours would it take to do the job if both of them worked together?

4. Ellen Hsu has baked a large batch of cupcakes for a bake sale. She ices them and sets them on a tray. She knows that it would normally take her 10 minutes to fill the tray with cupcakes. However, students are buying the cupcakes on the tray while she is icing new ones. Ellen iced and the students buy at constant rates. The tray is finally full after 25 minutes. If the students continue to buy at the same rate, how long will it take to sell a tray of cupcakes after Ellen stops icing?

5. When a large positive integer is divided by a smaller one, the integer part of the quotient is 3 and the remainder is 1. The sum of the integers is 29. Find the two integers.

6. By accident, 100 defective ligh bulbs  get mixed in with 900 good ones. There is no way to tell just by looking at the bulb whether it is good or bad.

  a. If a bulb is selected at random, what is the probability that it is bad? that it is good?
  b. If a sample of 20 bulbs is selected, what number would you expect to be bad?

7. If you flip a coin what is the probability that it lands heads up? Tails up?
   If you flip a coin 50 times, how many times would you expect it to land heads up?
   Flip a coin 50 times. Record the # of times it lands heads up. Were the actual results the same as you expected? (you do not need to flip it for me, i just need to know how to do the first 2 questions in this #7)  

Answer
1. 1/50 +1/x = 1/30 so x = 75 min
2. 1/5 -1/20 = 1/x so x = 20/3 hours
3. 1/3 +1/4 + 1/x so x = 12/7 hours
4. 1/10 -1/x = 1/25 so x = 100/6 minutes
5. x+y = 29 and x = 3y+1 so x = 22 and y = 7
6. a. 1 out of 10 bad, 9 out of 10 good
b. 2
7. obviously, 1 out of 2 heads, 1 out of 2 tails
25 heads out of 50 tries