A motorist averaged 40 miles per hour on his way to work. He averaged

Hi, You all canse use values as well and still get the answer

280 = 40 x time
time = 7

280 = 70 x time
time = 4

560 = speed x 11
speed = 560/11 or 50 10/11

Answer is B

Yes that was a silly mistake which I have now corrected. thanks.

A motorist averaged 40 miles per hour on his way to work. He averaged 70 miles per hour on his way home along the same route. Which of the following is the closest to his average speed for the round trip?

Average Speed = \(\frac{Total Distance}{Total Time taken}\)

Let distance from Home to Work be D. Therefore Total Distance = D+D = 2D

Time taken from Home to Work =\(\frac{Distance}{Speed}\) = \(\frac{D}{40}\)
Time taken from Work to Home = \(\frac{Distance}{Speed}\)=\(\frac{D}{70}\)

Therefore Total Time taken = \(\frac{D}{40}\)+ \(\frac{D}{70}\) = \(\frac{11D}{280}\)

Average Speed =\(\frac{2D}{11D/280}\) =\(\frac{2D * 280}{11D}\) =\(\frac{560}{11}\)= 50.9

Closest average speed to 50.9 for the round trip is 51.. Thus Answer B....

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Since the motorist traveled the same distance both ways, we can calculate his average speed by formula
{2*speed(journey to office)*speed(journey back home)}/Sum of speeds
=(2*40*70)/110
=560/11
=51 approximately(Option B)

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Average Speed = 2*S1*S2/(S1+S2)
=2*40*70/(40+70)
=560/11
=50.9 (approx)

Option B

We can use the following formula:

average rate = (total distance)/(total time)

If we let the distance between work and home = d, since time = distance/rate, his time going to work is d/40 and his time coming home from work is d/70. Thus:

average rate = 2d/(d/40 + d/70)

average rate = 2d/(7d/280 + 4d/280)

average rate = 2d/(11d/280)

average rate = 560d/11d = 560/11 ≈ 51

Answer: B

Hi All,

The answers to this question are 'spaced out' in such a way that you don't need to do much math at all to get to the correct answer. This prompt is a fairly common 'design' for a Weighted Average question. Here, a motorist travels a certain distance at one speed, then travels back - the SAME distance - at a different speed. We're asked for the AVERAGE SPEED for the entire trip.

One of the key elements to these types of questions is that the answer will be closer to the slower speed than to the faster speed. The exact 'middle' between 40 and 70 is 55, BUT since the motorist spends MORE time driving 40 mph, the average would have to be closer to 40 (while not being 40 exactly). There's only one answer that 'fits'...

Final Answer:

As an aside, GMAT question writers tend to be a bit 'savvier' with how they design the answer choices to these types of questions (meaning that it likely won't be quite this 'easy' to answer this type of question on Test Day)

GMAT assassins aren't born, they're made,
Rich

Average of both speeds = 40 + 70 = 55 m/h

As he took more time while traveling at 40 m/h than while he traveling at 70 m/h.

Then average speed must be more inclined towards slower speed (40 m/h), but it can't be exactly 40 m/h.

So answer is 51 m/h (B).

A motorist averaged 40 miles per hour on his way to work. He averaged 70 miles per hour on his way home along the same route. Which of the following is the closest to his average speed for the round trip?

A. 40
B. 51
C. 55
D. 59
E. 59.5
AVG SPEED= 2*a*b/(a+b)
where a = avg speed of motorist on his way to work.
b = avg speed of motorist on his way to home.

So answer is 50.9 which is equal to 51 m/h (B).

If you are given 2 speed and asked to find the average, you can use the below equation.

Equation :\( \frac{2*S1*S2}{S1+S2}\)

Here, 2 speeds are given.
S1 = 40
S2 = 70

Average speed =\(\frac{2*40*70}{40+70}\) = 50.9

Answer = B

Since the distance is the same 70*x=40*y with x and y as the different times needed.
Thus, x/y=4/7. Thus, the (weighted) average is: 70*(4/(7+4))+40*(7/(7+4)) ) = 50,9 (B)

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