GMAT Prep DS Q

[sudaif]

How many hours did it take Helen to drive from her house to her parents' house?

(1) Helen's average speed on this trip was 72 kilometers per hour
(2) If Helen's average speed on this trip had been 8 kilometers per hour greater, it would have taken her 1 hour less

statement 1 is clearly insuff

statement 2:

rt=1 ----eqt 1
(r+8)(t-1)=1-----eqt 2
when you simplify the two...you get to 8t^2-8t-1=0
I am unable to find the roots for this equation...
given that the discriminant is positive...there should be 2 roots
Thus, answer should be B

However, OA is C

[msbinu]

Let D be the total distance.

St 1
t1 = D/72

St 2
D/72 - D/80 =1

Simplifying this

8D/(80 * 72 ) = 1

8D = 80 * 72
D = 720

substituting the value of D in st 1
t1 = 720/72 = 10 hrs
:)

[sudaif]

thanks but still not sure what i'm doing wrong.
instructors, please?

[rohit801]

rt=1 ----eqt 1
(r+8)(t-1)=1-----eqt 2

Sudaif: Why do you have rt=1?

it should be rt=(r+8)(t-1), since the distance is the same (we don't know what it is)

This turns out to be r= 8(t-1). but we don't know r or t=>insufficient.

But taken together, we know what R is, so we can get T.

Hope this helps.

[RonPurewal]

Statement 2
rt=1 ----eqt 1
(r+8)(t-1)=1-----eqt 2

these aren't correct -- there's no reason why they should be set equal to 1, unless you know that the trip is exactly 1 kilometer long.

if you're going to use this sort of approach, then the only thing you can get out of statement 2 is
(r)(t) = (r + 8)(t - 1)
i.e., you know that these distances (= rate * time) are EQUAL TO EACH OTHER, but that's all you know -- you have no hard value (such as '1') to which you can equate them.

you can work with this:
rt = rt + 8t - r - 8
0 = 8t - r - 8
insufficient, since there are lots of solutions to this (remember, we don't need whole numbers).

if you have both statements, you have 0 = 8t - r - 8 and r = 72, which means you can find hard values for both r and t. therefore, sufficient together (don't bother finding the actual values), so (c).

[sudaif]

gotcha. thanks Ron. Not sure why i assumed d = 1

[tim]

:)