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A simple time pass puzzle:
Two taps are filling a bath. The first tap, by itself can fill the bath in one hour if the plug is in. The second tap can fill the bath in 30 minutes if the plug is in. With the plug out and both taps turned off, a full bath will empty in 45 minutes. How long does it take to fill an empty bath with both taps running and the plug out?
36 mins?
x/30+x/60-x/45=1
Sorry for the late response. Of course the answer is correct! :clap:
Next question:
A race course owner wants to install photoelectric timing device around his race track. The idea is to be able to conduct races & measure time taken for any race course length between 1000 metres to 31000 metres (in multiples of 1000 metres). Assume that he is free to conduct race in either direction of the race course. However the photoelectric timing device turns out to be pretty expensive. What is the minimum number of sensors required for his purpose and how should they be arranged?
No attempts? Guess I should explain the solution a bit more. Say if the length of the circular track is 3000 metres and the owner wants to conduct time tests for distance 1000 m or 2000 m, he can simply install two photoelectric device 1000 m from each other. For 2000 meter measurement he simply has to conduct race in the opposite direction.Quote:
Originally Posted by Benny Lava
Benny Lava: You have to state the assumptions clearly, unless I misunderstood! I have not been in a race in 60 years! :lol:
Do you need a photo sensor at the starting point?
Is the starting point fixed?
Depending on your answers to these questions the solutions will be different! :)
Hope you had a nice deepaavaLi ! :)
Quote:
Originally Posted by Benny Lava
Rajraj sir, Yes you are right. One sensor each at starting and ending point is needed to measure the time taken for each race. The starting point can be changed. The same photo electric sensor can be used as a starting point or an ending point. :)Quote:
Originally Posted by rajraj
More hints:
Take the 3000 meter circular race track, place one sensor at 0 meters( or 3000 meters if you go around) and another sensor at 2000 meters.
For a 1000 meter race start at the first sensor and end at the second sensor.
For a 2000 meter race start at the second sensor(at 1000 meters) and finish at the first sensor(at 3000 meters or 0 meters).
For a 3000 meter race start at the first sensor and finish at the same sensor going around.
You need only two sensors and you do not have to change directions. But you moved the starting point. That is the key - moving the starting point for different lengths!
Hope this helps in the 31000 meter race course problem! :)
While you are racing to solve the race course puzzle, here is something to relax! :)
On Sunday I watched the movie "A Disappearing Number", video taped version of the drama with the same title produced by the National Theatre(UK). It is about Ramanujan, the mathematician of the millennium. The number 1729 was in the movie. The conversation between Hardy and Ramanujan went somewhat like this when Hardy visited Ramanujan in the hospital.
Hardy: I rode in a taxi with the number 1729. An ordinary number
Ramanujan: No Hardy! It is a special number. It is the smallest number that can be exppressed as.............................
Fill in the blanks!
( Don't search the internet or run to the libray/bookstore for books on Ramanujan! :) )
Some more words of Ramanujan as hint:
Ramanujan: No Hardy! It is the smallest number that can be expressed as the sum of two___________________
Quote:
Originally Posted by rajraj
Yes. For a 31000 meter track, we have 30 different race distances to measure. If a combination of two sensors can measure for distance of N thousand meters, it can also be used to measure for distance of (31 - N) thousand meters. So essentially we need to have 15 combinations. 6C2 is equal to 15 hence 6 sensors are sufficient. Now the only problem is to decide how to place the 6 sensors such that all course lengths are covered :)Quote:
Originally Posted by rajraj