Thomas bought a train set with 25 toy engines that run at different speeds. The train set has five parallel tracks that can be built to race the engines. After each round, Thomas notes down the relative speeds of the engines instead of their actual lap times. What is the least number of races he can play before he can decide the first, second and third fastest engines?
Your Answer
a) 5
b) 7
c) 9
d) 3
don't give unnecessary answers I want the answer with explaintion
Answers
Answer:
I am shore 5.
Step-by-step explanation:
Given : Thomas bought a train set with 25 toy engines that run at different speeds.
The train set has five parallel tracks that can be built to race the engines. After each round, Thomas notes down the relative speeds of the engines instead of their actual lap times.
To Find :
What is the least number of races he can play before he can decide the first, second and third fastest engines
Solution:
Total 25 toy engines
and 5 parallel tracks
Hence in 1 race he can use maximum 5 toy engines and
in 5 races he will be able to race 25 engines ( 5 x 5 = 25)
As Speeds noted are relative so comparison between each set of 5 is required with all other set of 5 .
So he will take 1 fastest engine from each set and have a race of 5 engines .
With this race now he can have comparison between all 25 engines speeds.
So 6 is the least number of races he has to play before he can decide the first, second and third fastest engines
Another method can be
in 1 st race 5 engines then kepp 1 engine always in race and keep adding 4 from remaining in
Race Total Engines
1 5
2 5+ 4 = 9
3 9 + 4 = 13
4 13 + 4 = 17
5 17 + 4 = 21
6 21 + 4 = 25
All 25 engines in 6 races and results are compared with 1 engine Hence speed of all engines can be compared.
So 6 is the least number of races he has to play before he can decide the first, second and third fastest engines
Learn More:
Thomas bought a train set with 25 toy
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