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M08-02

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:36
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55% (hard)

Question Stats:

55% (01:01) correct 45% (01:04) wrong based on 129 sessions

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If it took a bus three hours to get from town A to town B, what was the average speed of the bus for the entire trip?

(1) During the first hour the bus finished $$\frac{1}{3}$$ of the distance at an average speed of 60 kilometers per hour.

(2) During the second hour the average speed of the bus was 80 kilometers per hour, twice its speed during the third hour.

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Joined: 02 Sep 2009
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16 Sep 2014, 00:36
Official Solution:

$$\text{Average speed}=\frac{\text{total distance}}{\text{total time}}$$, we know that total time is 3 hours, so we need to find the total distance.

(1) During the first hour the bus finished $$\frac{1}{3}$$ of the distance at an average speed of 60 kilometers per hour. $$\frac{1}{3}$$ of the distance is $$1*60=60$$ kilometers, hence the total distance is $$3*60=180$$ kilometers. Sufficient.

(2) During the second hour the average speed of the bus was 80 kilometers per hour, twice its speed during the third hour. During the second hour the bus covered 80 kilometers and during the third hour the bus covered $$\frac{80}{2}=40$$ kilometers, so during the last two hours it covered total of 120 kilometers. We don't know how many kilometers were covered during the first hour, hence this statement is not sufficient.

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Joined: 30 Apr 2014
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Location: India
Concentration: Marketing, Strategy
Schools: ISB '17 (A)
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22 May 2015, 05:57
What if the speed was different in the 2nd and 3rd hour? Wouldnt that change the average speed?
Math Expert
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22 May 2015, 06:45
1
syashveersingh wrote:
What if the speed was different in the 2nd and 3rd hour? Wouldnt that change the average speed?

All we needed to find the average speed was the distance, which from statement (1) turned out to be 180 kilometers. So, no, we are not concerned about the average speed during 2nd or 3rd hours.
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Joined: 13 Nov 2014
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10 Jun 2015, 09:17
Bunuel wrote:
If it took a bus three hours to get from town A to town B, what was the average speed of the bus for the entire trip?

(1) During the first hour the bus finished $$\frac{1}{3}$$ of the distance at an average speed of 60 kilometers per hour.

(2) During the second hour the average speed of the bus was 80 kilometers per hour, twice its speed during the third hour.

What a great question! It would be so easy to pick C thinking that you need stmt 2 to finish the math regarding stmt 1. But stmt 1 tells you that you are 1/3 of the way through after an hour at 60km. So we have to go 120 km in 2 hours or 180km in 3 hours, we have all we need for the average speed formula.

This question isn't a 700 because the math is difficult or niche, but because it is tricky.
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08 Jan 2016, 23:06
Bunuel wrote:
syashveersingh wrote:
What if the speed was different in the 2nd and 3rd hour? Wouldnt that change the average speed?

All we needed to find the average speed was the distance, which from statement (1) turned out to be 180 kilometers. So, no, we are not concerned about the average speed during 2nd or 3rd hours.

I still fail to understand
average speed of 1st hour was 60 not entire trip (which we need to find)
first - 60
second - 45
third 15
average speed changes!

Why 2nd & 3rd hour are not important?
Intern
Joined: 25 Dec 2012
Posts: 17

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11 Jan 2016, 18:31
paidlukkha wrote:
Bunuel wrote:
syashveersingh wrote:
What if the speed was different in the 2nd and 3rd hour? Wouldnt that change the average speed?

All we needed to find the average speed was the distance, which from statement (1) turned out to be 180 kilometers. So, no, we are not concerned about the average speed during 2nd or 3rd hours.

I still fail to understand
average speed of 1st hour was 60 not entire trip (which we need to find)
first - 60
second - 45
third 15
average speed changes!

Why 2nd & 3rd hour are not important?

It is the same for me. If the average speed in the second and third hour ara different will change the total average...
Intern
Joined: 29 Sep 2015
Posts: 6

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19 Jan 2016, 14:22
1
paidlukkha wrote:
Bunuel wrote:
syashveersingh wrote:
What if the speed was different in the 2nd and 3rd hour? Wouldnt that change the average speed?

All we needed to find the average speed was the distance, which from statement (1) turned out to be 180 kilometers. So, no, we are not concerned about the average speed during 2nd or 3rd hours.

I still fail to understand
average speed of 1st hour was 60 not entire trip (which we need to find)
first - 60
second - 45
third 15
average speed changes!

Why 2nd & 3rd hour are not important?

The important message in statement 1 is not that the average speed of the first hour was 60.
It's that 60km is one third of the total distance covered in 3hrsm so that the total distance is 180km.
Hence the avg speed is the total distance 180 divided by the total time, 3 hours.
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10 Mar 2018, 13:12
This is a good question but I don't consider it 700 level difficult. It's very easy to see that (i) provides enough information while (ii) does not.

I'm about a q48 level student and if I can solve this in less than a minute IMO it's not a 700 level Q
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Joined: 19 Jun 2017
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04 Jun 2018, 23:46
We only consider to calculate the average speeds when we have changing speeds in different parts of trip.
Here in statement 1 , if the answer is correct . It is assumed that the speed is constant through out the trip.
It is no where mentioned that the entire trip is made at a constant speed!!
I know we can calculate distance from st1 . But, we don't know the speed maintained in rest of the trip.

Please explain . There is no clarity.
Math Expert
Joined: 02 Sep 2009
Posts: 49320

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05 Jun 2018, 00:06
Richin wrote:
We only consider to calculate the average speeds when we have changing speeds in different parts of trip.
Here in statement 1 , if the answer is correct . It is assumed that the speed is constant through out the trip.
It is no where mentioned that the entire trip is made at a constant speed!!
I know we can calculate distance from st1 . But, we don't know the speed maintained in rest of the trip.

Please explain . There is no clarity.

The speed is not assumed to be constant. From (1) we know that in 1 hour the bus finished 1/3 of the distance at an average speed of 60 kilometers per hour. This implies that 60 kilometers is 1/3 of the distance, so the total distance is 180 kilometers.
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