6. A jar has 4 amoebas in it to start. Amoebas split their cells in two ( therefore doubling in size) once every minute. The jar will be completely filled in 10 minutes. How long would it take to fill the same sized jar if had 8 amoebas in it to start?
7. There are 100 golfers in the local match play contest. If a player loses a match, he is immediately eliminated from the contest. How many matches will be played to determine the winner?
8. Two trains are on a head on collision course. The trains are currently 65 miles apart. The north bound train is traveling at 55 miles per hour and the south bound train is traveling at 80 miles per hour. What is the distance between the trains two minutes before they collide?
9. A car travels at a speed of 30 mph over a certain distance, and then returns over the same distance at a speed of 20 mph. What is the average speed for the total trip?
10. A woman has 100 yards of cloth on a single roll, and she wants to divide it into 100 lengths of 1 yard each. It takes her 3 seconds to cut each length. Working non-stop, how long will it take her to cut all 100 pieces?
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7. There are 100 golfers in the local match play contest. If a player loses a match, he is immediately eliminated from the contest. How many matches will be played to determine the winner?
8. Two trains are on a head on collision course. The trains are currently 65 miles apart. The north bound train is traveling at 55 miles per hour and the south bound train is traveling at 80 miles per hour. What is the distance between the trains two minutes before they collide?
9. A car travels at a speed of 30 mph over a certain distance, and then returns over the same distance at a speed of 20 mph. What is the average speed for the total trip?
10. A woman has 100 yards of cloth on a single roll, and she wants to divide it into 100 lengths of 1 yard each. It takes her 3 seconds to cut each length. Working non-stop, how long will it take her to cut all 100 pieces?
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Answers:
6. 9 minutes
7. If there is to be only one winner, than there are 99 loses, therefore there were 99 matches. You can also do this with math: in round 1 there would be 50 matches to produce 50 winners, round 2 would have 25 matches to produce 25 winners, round 3 would have 12 matches to produce 12 winners ( one person of the 25 winners would have to wait until later to play again ), round 4 would have 6 matches to produce 6 winners, round 5 would have 3 matches to produce 3 winners, round 6 would have 2 matches ( the player left out before would now play to make it an even field ) to produce 2 winners, these 2 would play for the championship. So: 50+25+12+6+3+2+1=99
7a. ALTERNATE ANSWER
The first round is 50 matches eliminating 50 golfers, the second is 25 matches eliminating 25 golfers. For the third round the remaining 25 are divided into pools of 5 at random and face two matches each (each vs. a different randomly selected opponent in the pool). I think you will find that there will be two golfers and two only from each pool who will be dual winners. They will advance. The third round was then 5 pools of 5 matches so 25 more matches (100 total so far). The fourth round will be 5 matches eliminating 5 golfers. These five participate in a pool (fifth round) just like the third round (5 more matches and 2 emerge). The two play the championship match. So by round the matches are: 50+25+25+5+5+1 = 111 matches
8. If the trains are moving toward each other we combine their speeds to give us their speed basis. So: 55+80=135mph. Divide this speed by 60 minutes to give the speed they are traveling each minute=2.25 miles/minute. Therefore: 2 minutes before impact they are 4.5 miles apart.
9. 24 mph. Most people are quick to answer 25 mph, but this is not correct, as we will see. Let the distance traveled be 60 miles each way. Then, the trip out = 60/30 = 2 hours, and the trip back = 60/20 = 3 hours.
Therefore: the 120 mile trip = 120/5 = 24 mph.
10. The answer is 297 seconds, not 300 as most people would suppose. This is because the 100 pieces are made in 99 cuts. The last cut made results in 2 pieces instead of only one piece.
6. 9 minutes
7. If there is to be only one winner, than there are 99 loses, therefore there were 99 matches. You can also do this with math: in round 1 there would be 50 matches to produce 50 winners, round 2 would have 25 matches to produce 25 winners, round 3 would have 12 matches to produce 12 winners ( one person of the 25 winners would have to wait until later to play again ), round 4 would have 6 matches to produce 6 winners, round 5 would have 3 matches to produce 3 winners, round 6 would have 2 matches ( the player left out before would now play to make it an even field ) to produce 2 winners, these 2 would play for the championship. So: 50+25+12+6+3+2+1=99
7a. ALTERNATE ANSWER
The first round is 50 matches eliminating 50 golfers, the second is 25 matches eliminating 25 golfers. For the third round the remaining 25 are divided into pools of 5 at random and face two matches each (each vs. a different randomly selected opponent in the pool). I think you will find that there will be two golfers and two only from each pool who will be dual winners. They will advance. The third round was then 5 pools of 5 matches so 25 more matches (100 total so far). The fourth round will be 5 matches eliminating 5 golfers. These five participate in a pool (fifth round) just like the third round (5 more matches and 2 emerge). The two play the championship match. So by round the matches are: 50+25+25+5+5+1 = 111 matches
8. If the trains are moving toward each other we combine their speeds to give us their speed basis. So: 55+80=135mph. Divide this speed by 60 minutes to give the speed they are traveling each minute=2.25 miles/minute. Therefore: 2 minutes before impact they are 4.5 miles apart.
9. 24 mph. Most people are quick to answer 25 mph, but this is not correct, as we will see. Let the distance traveled be 60 miles each way. Then, the trip out = 60/30 = 2 hours, and the trip back = 60/20 = 3 hours.
Therefore: the 120 mile trip = 120/5 = 24 mph.
10. The answer is 297 seconds, not 300 as most people would suppose. This is because the 100 pieces are made in 99 cuts. The last cut made results in 2 pieces instead of only one piece.
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