There are two ways to solve this problem
Approach 1 -
This approach would require you to assume variables,write equations and solve them.
Yes! this approach take some time
Those of you who are new to math, would, most likely, attempt a question using this approach
First :
Convert the ratio into number by introducing a constant x
The speed
of the 3 runners will be 3x,4x and 5x.
Second
Assume the distance traveled by each runner is 60 units ( 60 is the LCM of 3,4,5.
You can take any number.. I took the LCM to avoid decimals.)
Speed =
distance/time. Hence Time =
distance/speed
Time will
be 60/3x,60/4x,60/5x. respectively = 20/x,15/x,12/x
Remove (1/x) and then you can write the numbers in a ratio: 20:15:12
Approach 2:
If you solve a mathematical question using this approach, it means you are comfortable
- determining the nature of numbers,
- identifying relationships between variables
- substituting values to arrive at an answer fast
This approach would take less time than approach 1.
Now lets solve this question using this approach
You would have observed the following in the question
- ratio of the speeds are given
- distant is constant
The relationship between speed and time is : Speed is
inversely proportional to time.
Hence if speed increases time decreases and vice versa.
The speeds are in the ratio 3:4:5.
Hence the times should be in the ratio: 1/3 :1/4: 1/5 as speed is inversely proportional to time.
Multiplying
with LCM (4,3,5) i.e. 60 ..............to normalize the ratio
We get 20:
15:12
The answer is 20:15:12
Take-away:
Always observe the hidden relationship between numbers
Watch this tutorial video and understand mathematical reasoning skills..
You can excel in math once you learn these skills.
Hope you understood both the methods.
Need math help: Get in touch with me:
My linkedin profile: https://www.linkedin.com/in/georgeanand
My facebook learning group: https://www.facebook.com/groups/semanticsGMAT
Want to explore math reasoning skills further try another problem
Solution here
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