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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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).

Time taken by Jonah to cover first half i.e 50 km of a 100 mile trip = x
time taken by Jonah to cover the second half i.e 50 km of a 100 mile trip = y
Total time taken by Jonah = x+y
Jonah's average speed for the entire trip =total distance /total time
=100/(x+y)
Answer B
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Hi Bunuel,

I have applied below approach :

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

curious to know flaw in my approach.

Thanks,

I see that is the answer, but what is wrong with adding two seperate speed and divide into two?

Posted from my mobile device

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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Adding to pushpitkc explanation:

Hi minji391, annusngh

Since time duration for both the speed is different so you can't simply add and divide it by 2.

Let me explain with some values.

For simplicity consider x = 5hrs and y = 10 hrs.

Speed during 1st half (S1) = 50/5 = 10 miles/hr

Speed during 2nd half (S2) = 50/10 = 5 miles/hr

Average speed = (S1+S2)/2 = (10 + 5)/2 = 7.5, which is wrong.

Actual average speed = 100/(10+5) = 6.66 miles/hr

Please note that time duration is different for each speed. So, you need to apply the weighted average formula.

Weighted average = (5*10 + 10*5)/(5+10) = 6.66 miles/hr.

Read following post for more detail:

weighted-averages

Hope it helps.

Must be (C), this is the end result of a formula



Source : https://www.veritasprep.com/blog/2015/0 ... -the-gmat/
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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:

GMAT assassins aren't born, they're made,
Rich
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Shouldnt we add the speeds separately ? like 50/x for 1st half + 50/y for second ?

why would this be wrong ?

\(Average speed = \frac{Total distance }{ time 1 + time 2}\)
Time 1 = x
Time 2 = y

\(Average speed = \frac{100 }{ x + y }\)

Answer B
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Hi a1997g,

There's a specific formula for Average Speed:

Average Speed = (Total Distance)(Total Time)

The reason why you can't just average the speeds in these types of questions is because (in almost all situations) you're dealing with a WEIGHTED Average.

For example, if you drive 60 miles at 60 miles/hour (re: 1 hour) and then another 60 miles at 30 miles/hour (re: 2 hours), then you spent far MORE time traveling 30 miles/hour. In this scenario, total distance = 120 miles and total time = 3 hours..... 120/3 = average speed of 40 miles/hour.

There is only one exception to this: when you travel each speed for the SAME amount of time. For example, if you drive 60 miles at 60 miles/hour (re: 1 hour) and then another 30 miles at 30 miles/hour (re: 1 hour), then total distance = 90 miles and total time = 2 hours..... 90/2 = average speed of 45 miles/hour (and this is the average of 60 and 30).

GMAT assassins aren't born, they're made,
Rich
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Total distance = 100 miles
Total time taken = x + y hours

Average speed = 100/(x+y) miles/hour

IMO B
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Average speed = Total distance/total time

Here, total distance 100 miles and total time is x+y

So, the Average speed = 100/x+y
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average speed = total distance / total time

average speed = 100 / x + y

lets say for example x = 2 y = 3

100 / 5 = 20 mph
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distance = rate * time
rate = distance / time

average speed = total distance / total time

total distance = 100
total time = x + y

100 / x + y

Answer is B.
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\(Average \ speed = \frac{Total \ Distance \ Traveled}{Total \ Time \ Taken}\)

Total Distance=100

Total time = x+y

\(Aaverage \ Speed = \frac{100}{x+y}\)

The answer is \(B\)
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