Susan drove an average speed of 30 miles per hour for the

Question

Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

A. 35
B. 40
C. 45
D. 50
E. 55

A. 35
B. 40
C. 45
D. 50
E. 55

Bunuel · Accepted Answer

average \ speed=\frac{total \ distance \ covered}{total \ time} ;

Total distance covered = 30 + 30 = 60 miles;
Total time = 30/30 + 30/60 = 3/2 hours;

average \ speed=\frac{total \ distance \ covered}{total \ time}=\frac{60}{\frac{3}{2}}=40 .

Answer: B.

Narenn · Answer

The Common Formula is Average speed = Total distance / Total time.
However if the distances traveled with two different speeds are the same (as 30 in this case), we can calculate the average speed as per following rule.
ratio of two distinct speeds = 1:2
Difference of two distinct speeds = 60 - 30 = 30
Now divide this difference by the sum of intergers of ratio (i.e. by 1+2 = 3 in this case ) 30/3 = 10
Average speed will be 10 X 1 part away from the lower speed i.e. 30 + 10 X 1 = 40.

The benefit of this method is once practiced enough you can calculate the average speed mentally or with minimal calculation and thereby can save valuable time on the GMAT

Regards,

Abhijit

tulsa · Answer

My approach:

30/30 -> 1h
30/60 -> 0.5h 
---------1.5h total and then 60/1.5 -> 40 (1.5 -> 3 -> 4.5 -> 6)

WholeLottaLove · Answer

Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

A. 35
B. 40
C. 45
D. 50
E. 55

What we have here are equal distances for both segments.

First segment: 30 miles/hour and covered 30 miles, therefore it took one hour.
Second segment: 60 miles/hour and covered 30 miles, therefore it took 1/2 hour.

(Total distance / total time)
(60 /  )
(60 / 1.5) = 40 miles avg. speed.

A. 35
B. 40
C. 45
D. 50
E. 55

(B)

When don't we simply add the distances/speeds together to get the average?

matthewsmith_89 · Answer

Hi  Bunuel ,

I don't know if this approach is right. I got the answer though

distance = speed x time
60 = (30 + 60) x time
60 = 90 x time
60/90 = time
2/3 multiplied by 60 = 40

Therefore, the answer is B. Is my approach correct?

Bunuel · Answer

No, that;'s not correct.

Distance = Average Speed * Time.

Distance = 60;
Time = 30/30 + 30/60 = 3/2 hours;

60 = Average Speed * 3/2

Average Speed = 40.

ScottTargetTestPrep · Answer

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 + ½)
 
average speed = 60/(3/2)
 
average speed = 40
 
Answer: B

EMPOWERgmatRichC · Answer

Hi All,

To figure out Average Speed for an entire trip, we need TOTAL Distance and TOTAL Time:

Total Distance = (Average Speed)(Total Time)

Here, we're given all of the numerical information we need to calculate each part of the journey:

1st part: 30 miles/hour for 30 miles

30 miles = (30mph)(Time) 
30/30 = T hours 
T = 1 hour

2nd part: 60 miles/hour for 30 miles 
30 miles = (60mph)(Time) 
30/60 = T hours 
T = 1/2 hour

Total Distance = 30 + 30 = 60 miles 
Total Time = 1 + 1/2 = 1.5 hours

Using these values, we can plug in and find the Average Speed for the entire trip:

60 miles = (Average Speed)(1.5 hours) 
60/1.5 = Average Speed

Average Speed = 40 mph

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

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

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

Answer: B

Cheers,
Brent

Tushrgupta · Answer

Can u help why is it not-

(30*30+30*60)/30+30 = 45
Since the average of speed is asked which is different in two equal horizons 
 
we can simply do 30+60/2 = 45

EMPOWERgmatRichC · Answer

Hi Tushrgupta,

Average Speed = (Total Distance)/(Total Time)

Thus, to determine the Average Speed for a trip, you need two specific pieces of information: TOTAL DISTANCE traveled and TOTAL TIME spent.

In this question, we know the TOTAL DISTANCE is 30 miles + 30 miles = 60 miles. However, the amount of TIME spent on each part of the trip is based on the SPEED. For the first 30 miles, we're traveling 30 miles/hour... so that is 1 hour of travel time. For the remaining 30 miles, we're traveling at 60 miles/hour... so that is just an additional 1/2 hour of travel time.

Total Distance = 60 miles
Total Time = 1.5 hours

Average Speed for this trip = (60)/(1.5) = 40 miles/hour

GMAT assassins aren't born, they're made,
Rich

100mitra · Answer

Avg Speed = {2*v1*v2} / {v1+v2}
v1 = 30
v2 = 60
Avg Speed = {2*30*60} / {30+60} = {3600 / 90} = 40

ThatDudeKnows · Answer

This gets you to the right answer, but I think it's a good example of a question where you can get to the same place faster (or at least as fast), more easily (or at least as easily...probably without even needing to write anything down), and with a lower risk of making a silly mistake.

30 miles at 30mph is one hour.
30 miles at 60mph is a half hour.
Total is 60 miles in 1.5 hours. That's 40mph.

Answer choice B.

No bonus points for elegance or using formulas that might be nifty/preferable in a coding exercise!

Sabuj40040 · Answer

average speed= 2*u*v/(u+v)=2*30*60/(30+60)=40

bumpbot · Answer

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