You cannot add add two different speeds and get an average speed.
Speed is total distance traveled by total time.
say the first half was done in 5 hrs ie. X=5 and second half was done in 25 hrs ie. y=25 then the total time would be 30 hrs.
So avg speed would be 100/30= 3.33 mph.
but according to what you tried it would become
{(50/5)+(50/25)}/2 --->
(10+2)/2=6 (which is incorrect).

Hi Bunuel,

I have applied below approach :

{ (50/X) + (50/Y) } / 2

curious to know flaw in my approach.

Thanks,

The mistake is that you are assuming the time to be equal for both the legs(thereby dividing it by 2 for final average speed)
Hence, If x=y, the formula you are using is correct.
However, if x>y or x<y, then the average speed will differ from the actual average speed.

Hope that helps!
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You've got what it takes, but it will take everything you've got

We are given that Jonah drove the first half of a 100-mile trip in x hours and the second half in y hours. We can determine average rate using the following equation:

average rate = total distance/total time

average rate = 100/(x + y)

Answer: B
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Hi All,

We're told that Jonah drove the first half of a 100-mile trip in X hours and the second half in Y hours. We're asked which of the following is equal to Jonah’s average speed, in miles per hour, for the entire trip. This question can be solved in a couple of different ways, including by TESTing VALUES.

Since we're dealing with the trip in two 50-mile pieces, we should TEST values for X and Y that divide evenly into 50. Let's TEST X=5 and Y=10
The first 50 miles were traveled in 5 hours.
The second 50 miles were traveled in 10 hours.
Total Distance = 100 miles and Total Time = 15 hours

Total Dist = (Av. Sp.)(Total Time)
100 miles = (Av. Sp)(15 hours)
100/15 = Av. Sp. = 6 2/3 miles/hour

Based on the design of the answer choices, we don't actually have to do that last extra calculation. Only one of the answers will equal 100/15 when you TEST X=5 and Y=10....

Final Answer:

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Rich
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