Susan drove an average speed of 30 mph for the first 30 min

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jbsocal: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu May 24, 2012 9:18 pm

by jbsocal » Tue Mar 19, 2013 8:08 pm

Susan drove an average speed of 30 mph for the first 30 minutes of a trip. She did drove 60 mph for the next 30 minutes. If she made no stops, what was the average speed, in miles per hour, for the entire trip?

a. 35
b. 40
c. 45
d. 50
e. 55

Could someone please explain why my logic is flawed?

If the driver drives at an avg rate of x miles per hour and the driver only drives half of 1 hour shouldn't the distance driven be 1/2 of what it would be if a driver drove for one full hour?

first 30 minutes
She drove at avg speed for 30 mph, so if she drove for 1hr then she would driven 30 miles
but she only actually drove for 30 minutes or so would she only have driven 15 miles since she drove have of an hour

Second 30 minutes
She drove at avg speed for 60 mph, so if she drove for 1hr then she would driven 60 miles
but she only actually drove for 30 minutes or so wouldn't she only have driven 30 miles since she drove have of an hour

So Total distance for 1 hours=

15 miles (half of 30 miles since she drove for 30 min)+30 miles (half of 60 miles since she drove for 30 min) = 45 miles

So avg rate is D/Time or 45miles/1 hour

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Source: Beat The GMAT — Problem Solving | Tue Mar 19, 2013 8:08 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Mar 19, 2013 8:57 pm

jbsocal wrote:Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. If she made no stops during the trip, what was Susan's average speed, in miles per hour, for the entire trip?

a. 35
b. 40
c. 45
d. 50
e. 55

Please note the words in red above, which reflect the wording of the original problem.
Time to travel the first 30 miles at a speed of 30mph = d/r = 30/30 = 1 hour.
Time to travel the remaining 30 miles at a speed of 60mph = d/r = 30/60 = .5 hours.
Average speed for the entire trip = (total distance)/(total time) = (30 + 30)/(1 + .5) = 60/1.5 = 40.

The correct answer is B.

Last edited by GMATGuruNY on Tue Mar 19, 2013 9:01 pm, edited 1 time in total.

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Tue Mar 19, 2013 9:01 pm

jbsocal wrote:Could someone please explain why my logic is flawed?

As per the question you've posted, your logic is flawless.
However, I feel the actual question is as follows...

Susan drove an average speed of 30 mph for the first 30 miles of a trip. She did drove 60 mph for the next 30 miles. If she made no stops, what was the average speed, in miles per hour, for the entire trip?

Total distance covered = (30 + 30) miles = 60 miles
Total time = (Time taken to cover 30 miles at 30 miles per hour) + (Time taken to cover 30 miles at 60 miles per hour) = 1 hour + 1/2 hour = 3/2 hours

Hence, average speed = (Total distance)/(Total time) = 60/(3/2) mph = 40 mph

The correct answer is B.

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jbsocal: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu May 24, 2012 9:18 pm

by jbsocal » Tue Mar 19, 2013 9:02 pm

GMATGuruNY wrote:
jbsocal wrote:Susan drove an average speed of 30 mph for the first 30 miles of a trip. She did drove 60 mph for the next 30 miles. If she made no stops, what was the average speed, in miles per hour, for the entire trip?

a. 35
b. 40
c. 45
d. 50
e. 55
Please note the words in red above, which reflect the wording of the original problem.
Time to travel the first 30 miles at a speed of 30mph = d/r = 30/30 = 1 hour.
Time to travel the next 30 miles at a speed of 60mph = d/r = 30/60 = .5 hours.
Average speed for the entire trip = (total distance)/(total time) = (30 + 30)/(1 + .5) = 60/1.5 = 40.

The correct answer is B.

my apologies for the typo, this clears up why B is correct.

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hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » Tue Mar 19, 2013 9:04 pm

jbsocal wrote:Susan drove an average speed of 30 mph for the first 30 minutes of a trip. She did drove 60 mph for the next 30 minutes. If she made no stops, what was the average speed, in miles per hour, for the entire trip?

a. 35
b. 40
c. 45
d. 50
e. 55

Could someone please explain why my logic is flawed?

If the driver drives at an avg rate of x miles per hour and the driver only drives half of 1 hour shouldn't the distance driven be 1/2 of what it would be if a driver drove for one full hour?

first 30 minutes
She drove at avg speed for 30 mph, so if she drove for 1hr then she would driven 30 miles
but she only actually drove for 30 minutes or so would she only have driven 15 miles since she drove have of an hour

Second 30 minutes
She drove at avg speed for 60 mph, so if she drove for 1hr then she would driven 60 miles
but she only actually drove for 30 minutes or so wouldn't she only have driven 30 miles since she drove have of an hour

So Total distance for 1 hours=

15 miles (half of 30 miles since she drove for 30 min)+30 miles (half of 60 miles since she drove for 30 min) = 45 miles

So avg rate is D/Time or 45miles/1 hour

Your method is accurate.

Average speed = Total distance / total time taken.

The flaw is already pointed out by GMATGuruNY.

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

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beatthe800: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Sat Feb 16, 2013 2:27 am; Location: India; Thanked: 1 times

by beatthe800 » Tue Apr 02, 2013 6:25 am

Here is my take,

If distance is constant
then
Avg speed = 2xy/ (x+y)
x= 30 mph
y= 60 mph

So Avg speed =40 (B)

Thanks,
Neil

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8183; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

hi

by Scott@TargetTestPrep » Tue Dec 12, 2017 3:51 pm

jbsocal wrote:Susan drove an average speed of 30 mph for the first 30 minutes of a trip. She did drove 60 mph for the next 30 minutes. If she made no stops, what was the average speed, in miles per hour, for the entire trip?

a. 35
b. 40
c. 45
d. 50
e. 55

We are given that Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. We must determine her average speed overall. The formula for average speed is:

average speed = total distance/total time

For the first half of the trip, we know that Susan's speed was 30 mph and her distance was 30 miles, so her time was 30/30 = 1 hour.

For the second half of the trip, we know that Susan's speed was 60 mph and her distance was 30 miles, so her time was 30/60 = 1/2 hour. Therefore her average speed in miles per hour is:

average speed = (30 + 30)/(1 + Â½)

average speed = 60/(3/2)

average speed = 40

Answer: B

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Dec 12, 2017 5:04 pm

jbsocal wrote:Susan drove an average speed of 30 mph for the first 30 minutes of a trip. She did drove 60 mph for the next 30 minutes. If she made no stops, what was the average speed, in miles per hour, for the entire trip?
a. 35
b. 40
c. 45
d. 50
e. 55

Average speed = (TOTAL distance)/(TOTAL time)

TOTAL distance
Susan traveled 30 miles at a speed of 30mph, and 30 miles at a speed of 60mph.
So, TOTAL distance = 60 miles

TOTAL time
TOTAL time = (time spent driving 30 mph) + (time spent driving 60 mph)
time = distance/speed
- Time spent driving 30 mph = 30 miles/30mph = 1 hour
- Time spent driving 60 mph = 30 miles/60mph = 0.5 hours
TOTAL time = (1 hour) + (0.5 hours) = 1.5 hours
----------------------------------

So, Average speed = (TOTAL distance)/(TOTAL time)
= 60 miles/1.5 hours
= 40 mph
= B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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