Problem Solving

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

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.

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.

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.

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