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Gloria Drives

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Gloria Drives

by sanju09 » Tue Feb 10, 2009 2:06 am
What was approximately the total distance in miles Gloria had to drive?

(1) Gloria drove half of her distance in 35 minutes and the remaining half at 50 miles per hour.

(2) Gloria achieved an overall average speed of 40 miles per hour.

OA :?:
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IMO C

by alto34 » Tue Feb 10, 2009 5:43 am
Hi,

My answer would be C.

This problem is to be solved with the classic equation: S = D / T

Statement A:
We do not know neither the average speed (S) nor the total time (T) it took her to reach her destination, so we can't calculate the total distance. STATEMENT A alone insuficient

Statement B:
we only know the Speed. So STATEMENT B alone insufficient.

But if we take both statement we can solve the problem.

From statement A we know that :
- it took her 35 minutes (T1) to drive 1/2 D
- the average speed during the second half of the trip (S2) was 50 miles / hour

From statement B we know that :
- the global average speed is 40 miles / hour (S), it is also:

S = (S1 + S2) / 2 where S1 is the speed during the first half of the trip.

40= (S1 + 50) / 2

S1 = 30 miles per/hour

Now we know S1, T1 so we can calculat D1 (wich is equivalent to 1/2 D)

1/2 D = S1 T1

D= 2 * 30 * 7/12

D= 35

So IMO C A and B

Am I right?
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Re: IMO C

by sanju09 » Wed Feb 11, 2009 3:56 am
alto34 wrote:Hi,

My answer would be C.

This problem is to be solved with the classic equation: S = D / T

Statement A:
We do not know neither the average speed (S) nor the total time (T) it took her to reach her destination, so we can't calculate the total distance. STATEMENT A alone insuficient

Statement B:
we only know the Speed. So STATEMENT B alone insufficient.

But if we take both statement we can solve the problem.

From statement A we know that :
- it took her 35 minutes (T1) to drive 1/2 D
- the average speed during the second half of the trip (S2) was 50 miles / hour

From statement B we know that :
- the global average speed is 40 miles / hour (S), it is also:

S = (S1 + S2) / 2 where S1 is the speed during the first half of the trip.

40= (S1 + 50) / 2

S1 = 30 miles per/hour

Now we know S1, T1 so we can calculat D1 (wich is equivalent to 1/2 D)

1/2 D = S1 T1

D= 2 * 30 * 7/12

D= 35

So IMO C A and B

Am I right?
:roll: C is right; but you are not!

First thing first: A, B, ..., E are answers; not statements, right? Write (1) or (2) for statements.

Next: Average speed is not the average of speeds.

Average Speed = Total Distance/Total Time. Although, you are not supposed to solve a DS problem till an answer; but when it comes to explanation, it should be precise, agree?

See it again:

What was approximately the total distance in miles Gloria had to drive?

(1) Gloria drove half of her distance in 35 minutes and the remaining half at 50 miles per hour.

(2) Gloria achieved an overall average speed of 40 miles per hour.

Given that each statement alone is not sufficient, we go for merger then.

If 2 d is total distance, in miles, then total time = [(35/60) + (d/50)] hours; and {2 d/[(35/60) + (d/50)]} = 40, would find your d, hence 2 d.

How was that :?:
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by moorthy76 » Wed Feb 11, 2009 4:37 am
great explanation Sanju09!!! thanks...
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Re: Gloria Drives

by x2suresh » Wed Feb 11, 2009 6:49 am
sanju09 wrote:What was approximately the total distance in miles Gloria had to drive?

(1) Gloria drove half of her distance in 35 minutes and the remaining half at 50 miles per hour.

(2) Gloria achieved an overall average speed of 40 miles per hour.

OA :?:

Invidual statements not sufficient
when combined
D/2 = S*35/60
D/2= 50*t -->(1)
D/(t+35/60) = 40 -->(2)

Solve 1 and 2 .. will get D..

C is the answer.
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