Brain teaser....Can you get them right (part 4) ?

Question

1.How can you measure 1 gallon of juice out of a barrel, if all you have available is a 3-gallon and a 5-gallon pitcher?

2.Two planes take off at the same exact moment. They are flying across the Atlantic. One leaves New York and is flying to Paris at 500 miles per hour. The other leaves Paris and is flying to New York at only 450 miles per hour. Which one will be closer to Paris when they meet?

3.In tossing a fair coin three consecutive times, what is the probability of getting heads on 2 consecutive tosses but NOT on three consecutive tosses?

What are your answers? And why?

Thanks for participating and have fun!

Answer 1

1. Fill the 3-gallon pitcher, then empty it into the 5-gallon pitcher. Fill the 3-gallon pitcher again, then empty just enough of it into the 5-gallon pitcher to top off the 5-gallon pitcher. The remainder in the 3-gallon pitcher is 1 gallon.

2. When they meet, no matter where they meet, they will be exactly the same distance away from Paris, or New York, or any other place in the world.

3. The chance to get two consecutive heads is (1/2)*(1/2)=1/4. The chance of getting the third consecutive heads is another *(1/2)=1/8. Thus the chances of the first but not the second would be (1/4)-(1/8)=1/8, or 12.5%.

Answer 2

1.
Fill 3-gallon pitcher, empty into 5-gallon pitcher, fill 3-gallon pitcher again and fill the rest of the 5-gallon from the 3-gallon, leaving 1 gallon in the 3-gallon pitcher.

2.
If they meet they are the same distance from Paris

3.
Required sequence HHT or THH. Total possible sequences = 2^3 = 8. Probability = 2/8 = 1/4

Answer 3

1) fill the 3 gallon barrel with 3 galons of juice and pour everything in the 5 gallon barrel.
The 5 gallon barrel now has 3 gallons in it.
Now fill the 3 gallon barrel with 3 gallons of juice and fill the 5 gallon barrel with the juice in the 3 gallon barrel.
The 3 gallon barrel has 1 gallon in it, and the 5 galon barrel is full.
done.
(there is another way of doing it by first filling the 5 gallon barrel, and emptying it in the 3 gallon barrel, but who cares... )

2) none... when they meet, they will be at the same place... so they will both be at the same distance from paris.

3) there are 8 possibles events when tossing a coin 3 times in a row (2 to the 3). and only 2 of them verify the conditions you want of them. : HHT, THH. Probability is therefore 1/4.

Answer 4

Two planes meet? With a combined air speed of 950 mph this is going to be one serious aviation accident. The plane leaving Paris would be closer by a plane length , at the instant the two noses collided.

Answer 5

1. Fill 3 gallon...dump it into 5 gallon...then fill it again an dump it again until 5 gallon is full an whatever is left is one gallon.

2. When they meet they are where they are...both close to Paris

3. 66.6%