In the morning, John drove to his mother's house in the

Question

In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

m09 q15

Bunuel · Answer

Official Solution:

In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

The average speed is equal to  \frac{	ext{total distance} }{	ext{total time} } .

Say the distance between the town and the village is  d  kilometers, and the speed from the village to town is  x  kilometers per hour, then  \frac{	ext{total distance} }{	ext{total time} }=\frac{d+d}{\frac{d}{60}+\frac{d}{x} } .  d  can be reduced, and we get  	ext{speed}=\frac{2}{\frac{1}{60}+\frac{1}{x} } . So, as you can see we only need to find the average speed from the village to town.

(1) In the evening, John drove at a constant speed of 40 kilometers per hour. Sufficient.

(2) John's morning drive lasted 2 hours. We know nothing about his evening drive. Not sufficient.

Answer: A

WholeLottaLove · Answer

In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

(1) In the evening, John drove at a constant speed of 40 kilometers per hour. 
When getting the average speed of two or more speeds, the distance (think of it like a weighted average) comes into play. In this case, the distance is the same for both speeds as he is traveling a route then traveling in the opposite direction on said route. 
SUFFICIENT

(2) John's morning drive lasted 2 hours. 
This allows us to get the distance of the route but we don't know how fast he drove on the return home.
INSUFFICIENT

(A)

nks2611 · Answer

statement 1. as distance is constant then we can apply direct formula 2xy/x+y= average rate here x=60 and y=40 then putting the values in formula we get 2*60*40/60+40= 48km/hr. hence suff.

statement2. no info. about another rate form village to town so insuff.

ScottTargetTestPrep · Answer

We are given that John drives at a rate of 60 km per hour and drives at a lesser rate when driving again later. We also are given that the distances driven are the same and need to determine the average rate.

We can use the formula:

average speed = total distance/total time

Statement One Alone:

In the evening, John drove at a constant speed of 40 kilometers per hour.

Since the distance each way is d, we can let time 1 = d/60, and time 2 = d/40; thus:

average speed = 2d/(d/60 + d/40)

average speed = 2d/(2d/120 + 3d/120)

average speed = 2d/(5d/120)

average speed = 240d/5d = 48

Statement one alone is sufficient to answer the question.

Statement Two Alone:

John's morning drive lasted 2 hours.

Knowing only the total time is not enough to determine the average speed.

Answer: A

gmatapprentice · Answer

ScottTargetTestPrep

Hi, can we use the formula 2S1S2/(S1+S2) to solve st. 1?

ScottTargetTestPrep · Answer

As a matter of fact, you can. In the formula average speed = 2d/(d/60 + d/40) that I used above, we can factor out d in d/60 + d/40 and we will get:

2d/

If we cancel d from the numerator and the denominator, we get:

2/(1/60 + 1/40)

Adding the two fractions in the denominator, we have:

2/((40 + 60)/(40*60)) = (2*40*60)/(40 + 60)

This is the exact same expression that you would get if you took S1 = 60 and S2 = 40 in your formula. You should note that this is only applicable when the distances traveled are the same for both speeds.

bumpbot · Answer

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