Nani traveled from her home to work at an average speed of 40 mph, and

Question

Nani traveled from her home to work at an average speed of 40 mph, and then immediately returned home. If Nani's average speed for the entire trip was 30mph, what was her average speed (in mph) while returning home?
A) 20
B) 22
C) 24
D) 26
E) 28

Source: GMAT Prep Now - https://www.gmatprepnow.com/module/gmat- ... /video/912

skylimit · Answer

My question: I understand the solution in the video. How do you use the "test the answers" strategy here?

zurvy · Answer

Hi Sky,

I don't think "picking the answers" is the efficient way to go (you'll waste time).

If you look at the final equation

1/40 + 1/x = 2/30 = 1/15

because 1/15 > 1/40, you have to pick a number for x so that 1/x becomes greater than 1/40.
Given the answer choices, all of them would satisfy that condition. So it's better to solve directly for x, which is here pretty simple.

MathRevolution · Answer

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Nani traveled from her home to work at an average speed of 40 mph, and then immediately returned home. If Nani's average speed for the entire trip was 30mph, what was her average speed (in mph) while returning home? 
A) 20
B) 22
C) 24
D) 26
E) 28

Let A be the time to take from Nani’s home to work, B be the return time and X be the return speed. Since the entire time is A+B, the distance from home to work is 40*A=X*B and that is the half of entire distance 30*(A+B)(--> 40*A=15(A+B)) and we have : 
40*A + X*B = 30(A+B)----*). 
By 40*A=15(A+B) we have :
5A=15B --> 5A=3B --> let A=3T, B=5T. 
Put these into *) we get :
40*(3T) + X*(5T)=30*8T by cancelling T at both sides --> 120+5X=240 --> 5X=120 --> x=24. 
The answer is C).

skylimit · Answer

I don't understand what T equals here. Does it equal A+B?
Also, what's the IVY approach?

praneet87 · Answer

I used a formula that was used for calculating average speeds.

2xy/x+y = average speed

80y/40+y=30
80y=1200+30y
y=1200/50=24

KarishmaB · Answer

Yes, you can use the formula of average speed when distance covered is the same. Average Speed = 2ab/(a+b) as done in the post above. Or you can use the "regular" average speed formula Average Speed = Total distance/Total Time = (d + d)/(d/40 + d/s)= 30 Note that all d's get cancelled and actually this equation comes down to the formula discussed above. Check this post for more on average speed discussion and these formulas: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/02 ... -the-gmat/

HKD1710 · Answer

Average speed = (Total distance) / (total time)

30 = 2D / (t1 + t2)

30 = 2D / (D/40 + D/s)

30 = 2/(1/40 + 1/s)

S = 24

ScottTargetTestPrep · Answer

We can let the distance to work = d, and the rate coming back = r. Thus:

average = (total distance)/(total time)

30 = 2d/(d/40 + d/r)

30(d/40 + d/r) = 2d

30d/40 + 30d/r = 2d

3/4 + 30/r = 2

Let’s multiply both sides of the equation by 4r:

3r + 120 = 8r

120 = 5r

24 = r

Answer: C

coylahood · Answer

Let the distance between her home and her work be 120 miles
Time taken to drive to work = 120/40 = 3 hours
Average Speed of the entire journey = 30mph
Let time taken to drive from home to work = x
Therefore, 30 = 240/(3+x)

30(3+x)=240
3+x = 8
x = 5 hours
Therefore average speed while returning home = 120/5 = 24mph

Abhishek009 · Answer

30 = \frac{2*S*40}{(S+40)}

3s + 120 = 8s

Or,  5s = 120

Or,  s = 24 , Answer must be (C)

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Nani traveled from her home to work at an average speed of 40 mph, and

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