Myra drove at an average speed of 30 miles per hour for some time and

Question

Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour?

(A) 1/5
(B) 1/3
(C) 2/5
(D) 2/3
(E) 3/5

Kudos for a correct solution.

(A) 1/5
(B) 1/3
(C) 2/5
(D) 2/3
(E) 3/5

Harley1980 · Accepted Answer

Let's name first part of distance F and second part S
We can make weighted average equation:
0.3F + 0.6S = 0.5(S + F)
0.1S=0.2F

\frac{S}{F}=\frac{2}{1}

So First part equal to  \frac{1}{3}  of all time

Answer is B

Lucky2783 · Answer

very simple application of weight average

30------50---60

W. Avg is 20 unit far from 30 and 10 unit far from 60 so

So at 60 mph she drove 2/3 of distance and at 30 mph she drove 1/3 of the distance.

Answer b

shriramvelamuri · Answer

my answer is 1/3.

Let the total distance be 1. The distance covered on 30mph= x; so the distance covered on 60 will be 1-x

<--------------------------------|---------->
 X (1-x)

Equating times,

x/30 + 1-x/60 = 1/50;

Solving we get, X= 1/5.= so distance covered at 30mph=1/5 and distance covered at 60mph=4/5

Time calculation,

Time taken to cover 1/5 jounery at 30mph= 1/150.

Total time taken for the entire jouney= 1/50.

Fraction of the time.

1/150/1/50 = 1/3 (option B).

Please correct me if wrong.

adityadon · Answer

50-30=20
60-50=10

Required answer is 10/(10+20) = 1/3

Zhenek · Answer

I concluded that time could serve as a variable that would let us divide the journey in fractions. Lets same time = 1. X - the fraction.
We can then conclude that, since the journey is the same and the total time is the same.
 30*x + 60*(1-x) = 50*1 
 30*x = 10 
 x = 1/3 
Which means the answer is B

SavageBrother · Answer

Average speed of 150:

30 + 60 + 60 = 150
150 / 3 = 50

1 hour of 30 miles an hour
2 hours of 60 miles an hour

30 miles an hour 1/3 of the time.

B.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Solution: We know the average speed and must find the fraction of time taken at a particular speed.

t1/t2 = (A2 – Aavg)/(Aavg – A1)

t1/t2 = (60 – 50)/(50 – 30) = 1/2

So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3.

Answer (B)

koreye · Answer

An alternate approach:

When i cannot figure out a direct way, I try the plug in approach, whcih usually means  picking one of the answers and plugging in to your model . I learnt this approach from Princeton Review's Cracking the GMAT which, IMO, is the only saving grace of Princeton Review's book.

fraction of time spent driving at 30 mph= x
fraction of time spent driving at 60 mph = y
Total time = T
d1 = distance travelled at 30 mph
d2 = distance travelled at 60 mph

chose 1/3 first because it just felt about right because avg of 50 mph is 20 more than 30mph and 10 less than 60...so I figured the portion of time spent driving at 60 mph should be longer.

which means

x/T = 1/3 (fraction of time spent driving at 30mph)
y/T= 2/3 (fraction of time spent driving at 60 mph)
Assume T to be 3 hours, then x = 1 hour, y= 2 hours (this works because we just need fraction, not exact or actual time)
which would make the distances =
d1 = 30 mph x 1 hr = 30 miles
d2 = 60 mph x 2 hrs = 120 miles
Total distance = 150 miles

finally confirm the answer with, avg speed = total distance/total time = 150/3 = 50 mph

which means 1/3 is correct

gracie · Answer

let t=total time
x=time @ 30mph
d=total distance
30x+60(t-x)=d
30x=60t-d
we know that d/50=t ➡ d=50t
substituting for d, 
30x=10t
x/t=1/3

ScottTargetTestPrep · Answer

We can use the formula of average speed = total distance/total time. We can let x and y be the first and second distances, respectively.

50 = (x + y)/(x/30 + y/60)

Multiplying by 60/60, we have:

50 = (60x + 60y)/(2x + y)

50(2x + y) = 60x + 60y

100x + 50y = 60x + 60y

40x = 10y

4x = y

Thus, the fraction of the time driving 30 mph was:

(x/30)/(x/30 + y/60)

Since y = 4x, we have:

(x/30)/(x/30 + 4x/60)
 
Multiplying by 60/60, we have:

2x/(2x + 4x)

2x/6x

1/3

Alternate Solution:

We can use a weighted average approach to answer this question. Had the average speed been 45 miles per hour, we would know that she traveled an equal amount of time at 30 mph and at 60 mph, since 45 is exactly halfway between 30 and 60. However, since the average speed was 50 miles per hour (which is closer to 60 mph than to 30 mph), we see that she traveled at 60 mph for a longer period of time. We see that 60 - 50 = 10 and 50 - 30 = 20, so if we break the trip into 3 segments, she traveled 2 of the 3 segments at 50 and 1 of the 3 segments at 30 mph. Thus, the fraction spent driving 30 mph is 1/3.

Answer: B

BrentGMATPrepNow · Answer

A student asked me whether it's possible to assign a "nice" value to the distance, and go from there. 
So, here it goes......

Let's say the total distance traveled =   300   miles

time = distance/speed 
Since the average speed for the entire trip is 50 miles per hour, the TOTAL travel time =   300  /50 =  6 hours

Let t = the time (in hours) Myra spent driving 30 miles per hour
So,  6  - t = the time Mrya spent driving 60 miles per hour

We know that: (distance traveled at 30 mph) + (distance traveled at 60 mph) =   300   miles
 distance = (rate)(time) 
So, we get: 30t + 60( 6  - t) =   300  
Expand: 30t + 360 - 60t = 300
Simplify: 360 - 30t = 300
Solve: t =   2

We now know that the entire trip took  6 hours , and that   2   of those hours were spent driving 30 miles per hour. 
So, the fraction of the total time spent driving 30 mph =   2  / 6  = 1/3

Answer: B

Cheers,
Brent

Abhishek009 · Answer

30 ________________________ 60

_____________ 50 _____________

10 ________________________ 20

= \frac{1}{3}  , Answer must be (B)

suganyamahendran · Answer

Can someone kindly guide where I missed.

k is the distance traveled in 30 miles

d
-------------- =50
(k/30)+ (d-k)/60

30*60 d
----------- = 50
60 k +30(d-k)

60d
--- = 50
k+d

60 d= 50k +50 d

d=5k

k/d= 1/5

Thanks a million in advance

yashikaaggarwal 
 KarishmaB 
 ChandlerBong 
 ThatDudeKnows 
 Bunuel 
 BrentGMATPrepNow 
 Narenn 
 walker 
 IanStewart

IanStewart · Answer

I think you (correctly) found what fraction of the total distance Myra drove at 30 mph, not what fraction of the total  time  she drove at 30 mph, which is what the question asks for.

KarishmaB · Answer

Ian has already pointed out the error in your solution so that's that. 
Also, average speed is the weighted average of speeds when weights are 'time taken' and hence this question can be directly solved using that concept.

VijayLisha · Answer

By using alligation method, I'm getting 1:2, But the ratio what we are getting is Speed,Right?

KarishmaB · Answer

Often learners know what to do but not why to do it. It doesn't work out in GMAT. The 'allegation method' or the scale method is used to average out a quantity. Here speed is averaged. The weights used are 'time for which each speed was maintained'. Since you are asked for the fraction of time 1:2 directly gives you 1/3 as the answer. To understand the basics of weighted averages, check out this post or the YouTube video, whichever format you prefer: https://anaprep.com/arithmetic-weighted-averages/ https://www.youtube.com/watch?v=_GOAU7moZ2Q

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Myra drove at an average speed of 30 miles per hour for some time and

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