An Alternative To The Quiz Questions.

[Kimmy]

Did you catch the train of did you miss it?


6 minutes and 18 seconds. The train has to effectively travel 5.25 miles at 50 mph. Time = Dist / Speed = 5.25 / 50 = 0.105 hours = 6.3 minutes = 6 minutes 18 seconds.

[Kimmy]

For those of us that caught the train its now time to board ship.


Puzzle 83

A ship is twice as old as the ship's boiler was when the ship was as old as the boiler is. What is the ratio of the boiler's age to the ship's age?

[BC]

Feb 13, 2010 9:52:53 GMT Kimmy said:

For those of us that caught the train its now time to board ship.


Puzzle 83

A ship is twice as old as the ship's boiler was when the ship was as old as the boiler is. What is the ratio of the boiler's age to the ship's age?

I can't get my head around that at all.

[BC]

I've just had a go at the train one though.

It takes 72 seconds for the train to cover 1 mile (nose to nose).
The nose of the tain has to travel 5 1/4 miles to be completely out.
5 1/4 x 72 secs = 378 secs = 6mins 18 secs.

Don't have long to wait to see if I'm right today!

[Kimmy]

3/4.

If we take the S to be the ship's age and B to be the boiler's age, and T to be the difference we get:

S - T = B

and

S = 2 x (B - T)

Eliminate T to get:

B / S = 3 / 4.

[Kimmy]

Fed up with the trains so I have taken my car.

Come on now all you 'lookers in' post your answer and be

Puzzle 84

After visiting my Great Aunt Anne, I travelled home in my old jalopy. The car was so old and battered, I was stuck in second gear. This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel. At the start of the journey I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour. As I arrived home, the car stopped because it had run out of fuel and I only just made it. How far was it from my Great Aunt's to my home?

[BC]

I shall have a go at this in bed with a cup of tea and post the answer in the morning... assuming I can work it out!

BC

[BC]

20 MPG means you use 1.5 gallons per hour at 30 MPH.
Add to that the 0.5 gallons per hour fuel loss means 2 gallons are used up per hour.
As there are 10 gallons, you travelled for 5 hours.

5 hours x 30 MPH = 150 miles to your Great Aunt Anne's house.

BC

[Kimmy]

150 miles: as I was travelling at 30 mph, I was using 1.5 gallons of fuel and losing 0.5 gallon of fuel for each hour I travelled. Therefore, I was getting through the fuel at a total rate 2 gallons per hour. Since I had 10 gallons of fuel at the start, I could travel for 5 hours before running out. 5 hours at 30 mph is 150 miles.

[Kimmy]

Did you get the last one right?

Don't get your feet wet on this one.

Puzzle 85

A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 6 small pipes, on their own, can drain the reservoir in 18 hours. How long will 6 large pipes and 6 small pipes take to drain the reservoir?

[BC]

Feb 16, 2010 12:11:13 GMT Kimmy said:

Did you get the last one right?

Don't get your feet wet on this one.

Puzzle 85

A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 6 small pipes, on their own, can drain the reservoir in 18 hours. How long will 6 large pipes and 6 small pipes take to drain the reservoir?

I have made a weird calculation that is almost certainly wrong. Anyway, here it is...

The essence of my peculiar thinking is that, if the pond held say 1200 litres, 600 litres would be drained by 6 big pipes in 6 hours and the small pipes would have drained 400 in that time, leaving 200.

The 200 is split between the two pipe sizes, this time leaving 33.33L in 1 hour. (That's 7 hours so far).

The 33.33L would be split and would take the big pipes 6 minutes to clear, the small pipes leaving 5.55L.

The 5.55 would be split and would take the big pipes 1 minutes to clear, the small pipes leaving 0.92L.

The 0.92L would be split and would take the big pipes 10 seconds to clear, the small pipes leaving 0.15L.

The 0.15L would take all pipes about 2 seconds, rounding up.

It makes the drainage time approx. 7 hrs 7 mins and 12 seconds.

No doubt the correct answer will be found using an easier method for sure !! Still, at least I had a go.

BC

[Kimmy]

7 hours and 12 minutes. The exact size of the pipes and reservoir does not matter. If we label the large pipes L, the small pipes S and if the reservior has a total of T litres, then:

T / 6L = 12 which means L = T / 72

and

T / 6S = 18 which means S = T / 108

we want

T / (6L + 6S) = T / ((6 x T / 72) + (6 * T / 108)) = 7.2 hours = 7 hours and 12 minutes.

[Kimmy]

Did you dip your toe in the last question?

I know you are looking in.

Now where did I put my truck?



Puzzle 86

A haulage contractor did not have room in his garage for 8 of his trucks. He therefore increased the size of his garage by 50 percent, which gave him room for 8 more trucks than he owned altogether. How many trucks did he own?

[BC]

Feb 17, 2010 12:12:07 GMT Kimmy said:

Did you dip your toe in the last question?

I know you are looking in.

Now where did I put my truck?



Puzzle 86

A haulage contractor did not have room in his garage for 8 of his trucks. He therefore increased the size of his garage by 50 percent, which gave him room for 8 more trucks than he owned altogether. How many trucks did he own?

I'm not too clever with equasions.

Actually, I'm not too clever full stop.

But anyway, I'll have a crack at it...

C = Capacity
T = Trucks owned

C = T - 8
and
C + (C / 2) = T + 8

So...

C + 8 = T
and
( C + (C / 2)) - 8 = T

The number I get to make both equasions correct is 40.

If he owns 40, and only has room for 32, this means he has 8 over. That works.

If he increases capacity by 50% from 32 to 48, then he has room for 8 more trucks than he owns.

BC

[Kimmy]

Being a duffer 'babminton' 'd' is also for 'dunce' and 'dumbo'
I wouldn't know where to start on these questions.


40 trucks: his original garage could hold 32 trucks. By increasing the size by 50%, the new garage could then hold 48 trucks - which is 8 more than he currently owned.

[Kimmy]

Right after messing about with the trucks lets get out in the fresh air.



Puzzle 87

4 shepherds were watching over their flocks and they were commenting on how many sheep they each had. If Alan had three more sheep, then he'd have one less sheep than Brian. Whereas Dave has the same number as the other three shepherds put together. If Charlie had three less sheep, he'd have exactly treble the number of Alan. If they were evenly distributed they'd each have eleven sheep. How man sheep does Alan have?

[liz]

87. Alan has 3 sheep. (Brian 7, Dave 22 and Charlie 12 = 44)

[BC]

Feb 18, 2010 13:24:50 GMT liz said:

87. Alan has 3 sheep. (Brian 7, Dave 22 and Charlie 12 = 44)

I agree.

[Kimmy]

3. If we denote Alan by A, Brian by B, Charlie by C and Dave by D we can find the answer in the following way. Since A + B + C = D and A + B + C + D = 44, it is easy to see that D has 22 sheep. So A + B + C = 22. We can use this along with the two other facts, A + 3 = B - 1 and C - 3 = 3A, to find that A has 3, B has 7, C has 12 and D has 22. In a little more detail:

A + B + C = 22 (1)
A + 3 = B - 1 (2)
C - 3 = 3A (3)

Rearrange (3) to give C = 3A + 3 and replace the C in (1) to give A + B + 3A + 3 = 22. Simplified this gives B = 19 - 4A (4). Rearrange (2) to give B - A = 4. Use (4) in the place of B to give 19 - 4A - A = 4 to give A = 3. Now use A to work out B, and then C.

[Kimmy]

Right, off to see Garndma again. Its her birthday.



Puzzle 88

You are your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?

[BC]

Feb 19, 2010 10:34:05 GMT Kimmy said:

Right, off to see Garndma again. Its her birthday.



Puzzle 88

You are your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?

Is this a trick question I wonder? I think the answer may be 2.

BC

[liz]

I think I agree BC - get to the first bridge give up one of 2 cakes and 1 is returned to you and so on.

[Kimmy]

2: At each bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

[Kimmy]

Off to the football match now.

Lets hope my team wins.

BUT before I can go I have got to solve this puzzle.

Puzzle 89

107 football teams compete in the annual cup shield. At the start of each round, the teams are selected in pairs, these pairs then compete against each other to determine who goes through to the next round. Any spare teams automatically go through to the next round. How many games must be played to determine the winner?

[BC]

Well, the way the rules are set out above, I'd say 106.

Round 1 = 53 games, 1 bye
Round 2 = 27 games
Round 3 = 13 games, 1 bye
Round 4 = 7 games
Quarter Final = 3 games, 1 bye
Semi Final = 2 games
Final = 1 game

BC

[Kimmy]

106: as there are 106 teams which must lose.

[Kimmy]

Whilst at the match I came across this incident.


Puzzle 90

A game of football with 11 players lasts for exactly 90 minutes. There are four substitutes that alternate equally. Therefore each player plays for the same length of time, how long?

[BC]

11 players are always on the pitch for 90 minutes, so 11 x 90 = 990 minutes

15 players take turns to cover the 990 minutes, so 990 / 15 = 66 minutes each.

BC

[liz]

I agree.

[Kimmy]

66 minutes: (11 * 90) / 15.