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

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New post 27 Feb 2018, 22:38
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anilnandyala wrote:
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

IMO B .i solved this question by box method attached bellow:-
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Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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New post 03 Apr 2018, 10:19
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anilnandyala wrote:
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


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

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New post 14 Apr 2018, 23:04
anilnandyala wrote:
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


Distance 1 = 30 miles

Speed 1 = 30 m/h

Time 1 = 30/30 = 1 hr

Distance 2 = 30 miles

Speed 2 = 60 m/h

Time 2 = 30/60 = 0.5 hr

Average speed = \(\frac{30 * 1 + 60 * 0.5}{1 + 0.5}\)

Avg Speed = 40 m/h

(B)
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New post 01 Oct 2018, 10:52
If one is able to understand concepts of speed correctly. They can note that this is not the arithmetic mean ever(unless distance and speed for both journey's are equal). Averaging of speed works on Harmonic Mean. That is :( 2 x A x B) /(A+B)

Where A and B are 2 speed. Works always whether a person is following to-fro motion or running same distance with diff speeds.

Do Note : This doesn't work when 2 distances are different.
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New post 03 Dec 2019, 08:21
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
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Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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New post 03 Dec 2019, 11:47
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

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Re: Susan drove an average speed of 30 miles per hour for the  [#permalink]

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New post 03 Dec 2019, 12:18
Saw this formula in another problem but seems applicable to this one too:

Formula used: Average speed = \(\frac{(p+q)∗(ab)}{(qa+pb)}\)

where the ratio of the distances traveled is p:q
speeds at which the respective distances are traveled are a and b

In this case we get \(\frac{(1+1)*(60*30)}{(60+30)}\)
Which is \(\frac{2*1800}{90} = 40 \)

Answer is B
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Re: Susan drove an average speed of 30 miles per hour for the   [#permalink] 03 Dec 2019, 12:18

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