A car traveled 75% of the way from town A to town B at an

Question

A car traveled 75% of the way from town A to town B at an average speed of 50 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?

A. 10
B. 20
C. 25
D. 30
E. 37.5

A. 10
B. 20
C. 25
D. 30
E. 37.5

Bunuel · Accepted Answer

Say the entire distance is 200 miles.
75% of the distance = 150 miles.
25% of the distance = 50 miles.

Total time = 200/40 = 5 hours;
Time spent to cover 150 miles = 150/50 = 3 hours.

Thus 50 miles was covered in 5-3=2 hours --> S = (speed) = (distance)/(time) = 50/2 = 25 miles per hour.

Answer: C.

subhendu009 · Answer

Let the distance from A to B be 200 miles.
75% of 200 miles = 150 miles.So time taken to cover that = 150/50 hrs = 3 hrs.  
So time taken to cover remaining distance = 50/s hrs.

Total time taken for the trip = 200/40 = 5 hrs.
so, 3 + 50/s = 5
 =>50/s = 2
 => s = 25

Hence,Option C will be the answer.
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amgelcer · Answer

Total distance = 100 miles (easier to work with %)
75% of the distance = 75 miles
25% of the distance = 25 miles

1st part of the trip → 75/50 = 1.5
2nd part of the trip → 25/S = t
Total trip → (75+25)/40 = 1.5 + t » 100/40 = 1.5 + t » 2.5 = 1.5 + t » t = 1

Back to 2nd part of the trip formula: 25/S = 1 » S = 25

Ans C

gunna · Answer

I just solved it algebraically, and better believe me - Assuming a Value for the Distance is way faster.

ronr34 · Answer

I tried to solve it a different way... using weighted averages but hit a wall...
Can you see where my logic fails?

Since the first part of the trip was 3/4 and the last was 1/4, this is what I got in my diagram:

S-----40-----50

----1-----3-----

When doing the cross multiplication, I get (50-40)/(40-S) = 3/1 -> I get S=110/3.

Why is this failing?

KarishmaB · Answer

The weight when calculating average speed is time, not distance. This means that when you write (50-40)/(40-S) = 3/1, you are assuming that the car traveled 75% of the TIME at speed S and 25% of the time at speed 50 mph. Ratio of 'Distance traveled' cannot act as the weight. See this post for a discussion of this concept: bill-travels-first-40-of-the-distance-to-his-destination-at-137000.html#p1172411 For this question, use the regular formula: Avg Speed = Total Distance/Total Time = \frac{100}{75/50 + 25/S} = 40 This gives S = 25 mph

PareshGmat · Answer

Setting up the equation for time

Total time consumed in the Journey = Addition of time of individual journeys

Refer the diagram below

ravih · Answer

Hey Bunuel,

How do we know when is it ok to plug in an assumed value? In this case, I was hesitant to plug in a value thinking that it may impact the calculation wrongly. Also, there simply isnt enough time to plug in 2 values and check if they each give the same answer!

Bunuel · Answer

Well, the question talks only about the percentages of the total distance, so whatever the actual distance is the answer must remain the same.

GMatAspirerCA · Answer

Some where i read that average speed = 2s1*s2/(s1+s2). Clearly this is not applicable in current scenario. Can some one recollect when does this average speed formula holds good?

KarishmaB · Answer

It applies when the distance traveled at the two speeds is the same.

100 km at 50 kmph
100 km at 100 kmph

Avg speed = 2*50*100/(100+50) = 66.7 kmph

Avg Speed = 200/3 = 66.7 kmph

GMatAspirerCA · Answer

Thanks Karisma. I donot have many kudos to give away. but your reply meant alot to clarify concepts.

TaN1213 · Answer

let D = 100
average speed = total distance / (T1 + T2)
T1 =75/ 50 = 3/2 ----> time taken to cover first part of the journey
T2 = 25/S ----> time taken to cover second part of the journey

Substituting 
40 = 100/(3/2 + 25/S)
S = 25
IMO C

varun4s · Answer

Let distance= 100

Time taken to cover first part of the journey=  \frac{75}{50}

................................second part..................=  \frac{25}{S}

Average Speed=  \frac{Total Distance}{Total Time}

40= 100/( \frac{3}{2} + \frac{25}{S} )

Solving

S= 25

Answer: C.

bumpbot · Answer

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A car traveled 75% of the way from town A to town B at an

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