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Tough and tricky Rate problem......Expert needed

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Tough and tricky Rate problem......Expert needed

by Mo2men » Thu Dec 29, 2016 1:12 pm
If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?


(1) In the first 2 hours the bus covered 100 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half.

i do not completely how the OA is E???

Source: GMATCLub tests

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Last edited by Mo2men on Thu Dec 29, 2016 9:44 pm, edited 1 time in total.
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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Thu Dec 29, 2016 2:19 pm
Mo2men wrote:If it took a bus 4 hours to get from town AA to town BB, what was the average speed of the bus for the trip?


(1) In the first 2 hours the bus covered 100 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half.

i do not completely how the OA is E???

Source: GMATCLub tests

Thanks
The information in statement 2 is about the average speed for the first half of the distance, not the first half of the time. The trap is thinking "oh, well it was 50mph for the first 2 hours and 25 mph for the next 2!" But that scenario won't satisfy statement 2, as 100 miles would be covered at 50mph and 50 miles would be covered at 25 mph. (So 100 miles is not, in fact, half the overall distance.) In actuality, we have no idea what the distance for the whole trip was (we just know it was more than 100 miles.)
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by Jay@ManhattanReview » Fri Dec 30, 2016 4:06 am
Mo2men wrote:If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?


(1) In the first 2 hours the bus covered 100 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half.

i do not completely how the OA is E???

Source: GMATCLub tests

Thanks
S1: Statement 1 itself in not sufficient since we do not know the distance the bus traveled in the concluding 2 hours.

S2: Say the total distance between A and B = 2D miles and the average speed of the bus for the first half = 2x mph and the average speed of the bus for the second half = x mph.

=> Total time = 4 = Time taken to cover the first half (D) + Time taken to cover the second half (D)

=> 4 = D/2x + D/x

=> x = 3D/8: Insufficient.

S1 and S2 together: Even after combining both the statements, we cannot get the answer since the information in S1: 'In the first 2 hours the bus covered 100 miles.' cannot be taken as D = 100 miles. Insufficient.

Hope this helps!

-Jay
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by GMATGuruNY » Fri Dec 30, 2016 10:27 am
Mo2men wrote:If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

(1) In the first 2 hours the bus covered 100 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half.
Statement 1:
Average speed for the first 2 hours = d/t = 100/2 = 50mph.
Since the average speed for the last 2 hours is unknown, the average speed for the entire trip cannot be determined.
INSUFFICIENT.

Statement 2:
Rate and time have a RECIPROCAL relationship.
Since the rate for the first half of the distance is TWICE the rate for the second half of the distance, the time for the first half of the distance is 1/2 the time for the second half of the distance.
In other words:
(time for the first half of the distance) : (time for the second half of the distance) = 1:2.
Implication:
1/3 of the total time of 4 hours -- in other words, 4/3 hours -- is spent traveling the first half of the distance.
2/3 of the total time of 4 hours -- in other words, 8/3 hours -- is spent traveling the second half of the distance.
Since the actual speeds are unknown, the average speed for the entire trip cannot be determined.

Statements combined:
The average speed for the first 2 hours (Statement 1) tells us nothing about the average speed for the first 4/3 hours (Statement 2).
Thus, the average speed for the entire trip cannot be determined.
INSUFFICIENT.

The correct answer is E.
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by Mo2men » Sat Dec 31, 2016 10:19 pm
GMATGuruNY wrote:
Statement 1:
Average speed for the first 2 hours = d/t = 100/2 = 50mph.
Since the average speed for the last 2 hours is unknown, the average speed for the entire trip cannot be determined.
INSUFFICIENT.

Statement 2:
Rate and time have a RECIPROCAL relationship.
Since the rate for the first half of the distance is TWICE the rate for the second half of the distance, the time for the first half of the distance is 1/2 the time for the second half of the distance.
In other words:
(time for the first half of the distance) : (time for the second half of the distance) = 1:2.
Implication:
1/3 of the total time of 4 hours -- in other words, 4/3 hours -- is spent traveling the first half of the distance.
2/3 of the total time of 4 hours -- in other words, 8/3 hours -- is spent traveling the second half of the distance.
Since the actual speeds are unknown, the average speed for the entire trip cannot be determined.

Statements combined:
The average speed for the first 2 hours (Statement 1) tells us nothing about the average speed for the first 4/3 hours (Statement 2).
Thus, the average speed for the entire trip cannot be determined.
INSUFFICIENT.

The correct answer is E.
Dear GMATGuru,

When both statements combined, we know for certain that the bus traveled 4/3 of the 2 hrs with an average speed V1. Can you come up with different numbers/scenarios that make both yield different distances and hence make both statements insufficient. I tried hard but failed.

Thanks
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by GMATGuruNY » Sun Jan 01, 2017 8:51 am
Mo2men wrote:
GMATGuruNY wrote:
Statement 1:
Average speed for the first 2 hours = d/t = 100/2 = 50mph.
Since the average speed for the last 2 hours is unknown, the average speed for the entire trip cannot be determined.
INSUFFICIENT.

Statement 2:
Rate and time have a RECIPROCAL relationship.
Since the rate for the first half of the distance is TWICE the rate for the second half of the distance, the time for the first half of the distance is 1/2 the time for the second half of the distance.
In other words:
(time for the first half of the distance) : (time for the second half of the distance) = 1:2.
Implication:
1/3 of the total time of 4 hours -- in other words, 4/3 hours -- is spent traveling the first half of the distance.
2/3 of the total time of 4 hours -- in other words, 8/3 hours -- is spent traveling the second half of the distance.
Since the actual speeds are unknown, the average speed for the entire trip cannot be determined.

Statements combined:
The average speed for the first 2 hours (Statement 1) tells us nothing about the average speed for the first 4/3 hours (Statement 2).
Thus, the average speed for the entire trip cannot be determined.
INSUFFICIENT.

The correct answer is E.
Dear GMATGuru,

When both statements combined, we know for certain that the bus traveled 4/3 of the 2 hrs with an average speed V1. Can you come up with different numbers/scenarios that make both yield different distances and hence make both statements insufficient. I tried hard but failed.

Thanks
Case 1: 60 miles traveled in the first 4/3 hours, implying a total distance of 120 miles
Since the distance traveled in the first 2 hours = 100 miles, the distance traveled in the next 2/3 hour = 40 miles.
Remaining distance traveled in the last 2 hours = 20 miles.
Average speed for the entire trip = (total distance)/(total time) = 120/4 = 30mph.

Case 2: 80 miles traveled in the first 4/3 hours, implying a total distance of 160 miles
Since the distance traveled in the first 2 hours = 100 miles, the distance traveled in the next 2/3 hour = 20 miles.
Remaining distance traveled in the last 2 hours = 60 miles.
Average speed for the entire trip = (total distance)/(total time) = 160/4 = 40mph.
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