Mental Puzzles

aphexcoil

aphexcoil

Tom and Henry have a 100 meter race and Tom manages to finish the race with Henry still 5 meters behind. They both agree to race again, but this time Tom will start 5 meters behind the starting line to give Henry a chance. Both runners run the second race exactly as the first.

Who won the second race?
 
Tommy Boy must've been going faster to beat the other guy the first time, so at 5 meters before the end of the second race, they were neck and neck. Since Tommy was going faster, he finished first again.
 
Quote from aphexcoil:

Tom and Henry have a 100 meter race and Tom manages to finish the race with Henry still 5 meters behind. They both agree to race again, but this time Tom will start 5 meters behind the starting line to give Henry a chance. Both runners run the second race exactly as the first.

Who won the second race?
More...

Race 1 (100m all)
Tom covers 100m to Henry's 95m.
Tom 1 : .95 Henry

Race 2 (105m for Tom, 100m for Henry)
Tom does 1 * 105 m = 105 m (100m course + 5m delay)
In the time that Tom covers his 105m, Henry only covers 105m * .95 = 99.75m

So, Tom wins again, except this time by .25m instead of 5m (as in race 1). Also, we assume Tom can run his extra 5m at the same pace as the first 100m.

Correct, or not?
 
Quote from hardrock375:



Race 1 (100m all)
Tom covers 100m to Henry's 95m.
Tom 1 : .95 Henry

Race 2 (105m for Tom, 100m for Henry)
Tom does 1 * 105 m = 105 m (100m course + 5m delay)
In the time that Tom covers his 105m, Henry only covers 105m * .95 = 99.75m

So, Tom wins again, except this time by .25m instead of 5m (as in race 1). Also, we assume Tom can run his extra 5m at the same pace as the first 100m.

Correct, or not?
More...

You got it!

Tom runs 100 meters for every 95 meters Henry runs. So the equation I used was:

100/95 = 105 / X

cross multiply and you get 100X = 9,975

X = 99.75

Therefore, after Tom runs his 105 meters, Henry has only covered 99.75 meters of the race.


Anyone got any puzzles?
 
There is a system for pricing these items. Please determine how much the chocolate should cost.

ICE CREAM -- 32 cents
LOLLIPOP -- 34 cents
JAWBREAKER -- 42 cents
GUM -- 13 cents
CHOCOLATE -- ?? cents
 
Quote from aphexcoil:

There is a system for pricing these items. Please determine how much the chocolate should cost.

ICE CREAM -- 32 cents
LOLLIPOP -- 34 cents
JAWBREAKER -- 42 cents
GUM -- 13 cents
CHOCOLATE -- ?? cents
More...

My guess is
Vowels are worth 3 cents
Consonants are worth 5 cents

So...
3v + 5c = ans.

Ice Cream = 3*4 + 5*4 = 32
Lollipop = 3*3 + 5*5 = 34
Jawbreaker = 3*4 + 5*6 = 42
Gum = 3*1 + 5*2 = 13
Chocolate = 3*4 + 5*5 = 37

Chocolate is priced 37 cents.

P.S. My friend Matt, a.k.a. "The Weaseler" gave me assistance on this one.
 
I did it a little differently.

Time is constant

Distance
Tom = 100
Henry = 95

difference = 5

95/5 = 19

Tom runs Henry+1/19 Henry

105/ 1+(1/19) = 99.75
 
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