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Hello Sir,
I have understood the question and the answer to it. However, this question has put questions on my understanding.
For "Averages", we take the ratios. I have always understood that when it is average speeds, ratio of "time" needs to be taken and not the ratio of "distances". But here by ratio of distances, we are able to arrive at the average speed. Has my understanding been wrong?
Please assist.
No, your understanding isn't wrong.
If we are given the speeds and the ratio of distances, we can still figure out the ratio of 'times'.
The average speeds are 80 and 60 kmph.
Say the distance from
A to B is 120 km
B to C is 30 km
Then, the time taken from
A to B would be 1.5 hours
B to C would be 0.5 hours
The two times are in a ratio of 3:1
Even if you take some other distances, the ratio would remain the same.
The average speeds are 80 and 60 kmph.
Say the distance from
A to B is 240 km
B to C is 60 km
Then, the time taken from
A to B would be 3 hours
B to C would be 1 hour
Ratio of 3:1
Basically, if the distances are 4x and x km, and the speeds are 80kmph and 60kmph, , the times would be in the following ratio:
4x/80 : x/60
--> 1/20 : 1/60
--> 60 : 20
--> 3 : 1