M16-08

Question

If a bus took 6 hours to travel from town A to town B, what was its average speed for the entire trip?

(1) In the first 2 hours, the bus covered a distance of 150 miles.
 
(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

Bunuel · Accepted Answer

Official Solution:

If a bus took 6 hours to travel from town A to town B, what was its average speed for the entire trip? 
 
(1) In the first 2 hours, the bus covered a distance of 150 miles.
 
This information provides the average speed of the bus for the first 150 miles, which was 75 miles per hour. However, we don't know its average speed for the remaining 4 hours of the journey. Not sufficient.
 
(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.
 
This statement implies that the bus covered the first half of the distance in half the time it took to cover the second half of the distance. Since the journey took a total of 6 hours, the bus took 2 hours to cover the first half of the distance and 4 hours to cover the second half of the distance. Not sufficient.
 
(1)+(2) From (1), we know that in the first 2 hours, the bus covered a distance of 150 miles. From (2), we know that it took the bus 2 hours to cover the first half of the distance. Consequently, the entire journey was 300 miles long. As it took 6 hours to cover this distance, the average speed for the entire trip was 300/6 = 50 miles per hour. Sufficient.

Answer: C

patto · Answer

I think this is a  high-quality  question and I agree with explanation.

DiCaprio25 · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Ashu101 · Answer

Why do we assume that first half of the distance is 150 miles. As nowhere it is mentioned that the first 2 hours of the trip has covered half of the distance. Please can I get a more detailed explanation for this.

Bunuel · Answer

Read carefully:

(1)+(2) From (1), we know that in the  first 2 hours , the bus covered a distance of  150 miles . From (2), we know that it took the bus  2 hours  to cover the first  half of the distance . Consequently, the entire journey was 300 miles long. As it took 6 hours to cover this distance, the average speed for the entire trip was 300/6 = 50 miles per hour. Sufficient.

first 2 hours  -->  150 miles 
 2 hours  -->  half of the distance

Hence,  150 miles  =  half of the distance .

rickyric395 · Answer

We need  Avg(speed)=\frac{total distance}{total time taken} 
Statement 1: in first 2 hrs, bus covered 150miles, here speed =  \frac{150}{2}=75 miles/hr. We know nothing about distance in next 4 hrs. Hence Insufficient.

Statement 2: Speed in first half is 2 times speed in second half . Let total distance be  d . We know speed is inversely proportional to time if distance is constant  speed=\frac{distance}{time} ]. Here distance is same. So we can say 2t1=t2. We know  t1+t2=6 . Hence t1=2, and t2=4.
But again no info on distance. Hence insufficient.

Both : We know t1=2hrs, and we know first half takes 2 hrs (inferred from statement 2), so obviously second will also be 150 miles.
Using  Avg(speed)=\frac{total distance}{total time taken} ;  speed=(150+150)/6 =50miles/hrs.

C is the answer

r_putra_rp · Answer

Hi  Bunuel

I still can't get the logic as to the logic of getting the amount of total distance, there seems to be a jump from 150 from statement (1) to the 300 in the (1)+(2)

Analyzing your statements
- "From (1), we know that in the  first 2 hours , the bus covered a distance of  150 miles "
sure, I have no problem

- "From (2), we know that it took the bus  2 hours  to cover the first  half of the distance "
There is nowhere in the text that indicates the two hours from the first statement is the actual distance, statement (1) only says that it  takes 2 hours and a 150 miles , nothing about the 150 miles being half of the distance. Thus, since we don't know the remaining distance, we cannot get the average.

It would be different if statement (2) said that it took 2 hrs to reach half of the distance eg "The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance  and the bus took 2 hrs to cover half the distance"

or statement (1) said that the 150 is half of the distance eg "In the first 2 hours, the bus covered a distance of 150 miles  which is half of the distance required "
There is a disconnect between the two

please advise

Bunuel · Answer

(1) says: In the FIRST 2 hours, the bus covered a distance of 150 miles.
(2) says: The bus took 2 hours to cover the FIRST HALF of the distance and 4 hours to cover the SECOND HALF of the distance.

(1)+(2) In the FIRST 2 hours, in which the bus covered the FIRST HALF of the distance, the bus covered a distance of 150 miles. Consequently, the entire journey was 300 miles long. As it took 6 hours to cover this distance, the average speed for the entire trip was 300/6 = 50 miles per hour. Sufficient.

Hope now it's clear.

Ak9sh · Answer

What a beautiful question!

anm_awesome · Answer

What an awesome question - really challenges every muscle of your brain - thank you for your efforts - keep delighting us

mellowmev · Answer

I think this is a high-quality question and I agree with explanation.

Paattaa · Answer

I like the solution - it’s helpful.

M16-08

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