I have attached the question as an image. I started off by setting both the downstream and upstream equations to each other since they both have the same 'd' (distance) ( d = s * t ) .
Help me solve this GMAT Quant Question (GMATPrep)
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- EricImasogie
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- MartyMurray
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Let's try that way.
We start with rate(r) * time(t) = distance(d), and get two equations.
(v - 3)(t + 1/2) = 90 and (v + 3)(t) = 90
Now we can set them equal to each other, because they both equal 90.
(v - 3)(t + 1/2) = (v + 3)(t)
Multiply it all out.
vt + v/2 - 3t - 3/2 = vt + 3t
Simplify.
v/2 - 3/2 = 6t
v - 3 = 12t
Now we can substitute the 12t for (v - 3) in the upstream equation and solve for t.
(12t)(t + 1/2) = 90 12t^2 + 6t = 90 2t^2 + t = 15 2t^2 + t - 15 = 0 (2t - 5)(t + 3) = 0
t = -3 or 2.5. Throw out the - 3, at least in this universe. Choose A.
That's a fair amount of work. Wondering if there is a better way.
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- Brent@GMATPrepNow
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I like to begin with a "word equation." We can write:A boat travelled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then travelled downstream at an average speed of (V+3) miles per hour. If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?
A) 2.5
B) 2.4
C) 2.3
D) 2.2
E) 2.1
travel time upstream = travel time downstream + 1/2
Time = distance/rate
So, we can replace elements in our word equation to get:
90/(v-3) = 90/(v+3) + 1/2
Now solve for v (lots of work here)
.
.
.
v = 33
So, travel time downstream = 90/(v+3)
= 90/(33+3)
= 90/36
= 5/2
= 2 1/2 hours
Answer: A
Cheers,
Brent
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For the record, I thought maybe I had found a simpler way, and the new way still took about the same amount of work and came down to the same quadratic equation to factor.
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Hi EricImasogie,
This question can be solved by TESTing THE ANSWERS, but you still have to take lots of notes and stay organized.
First, we have 2 equations that we need to write down (they both involved the Distance Formula and the given 90 mile distance):
Upstream:
90 = (V-3)(T + 1/2)
Downstream:
90 = (V+3)(T)
Since we're multiplying two different sets of values and the product is 90 in both equations, it's highly unlikely that we'll be dealing with a "weird" decimal - we need to end up with round numbers, so the value that I would TEST first is 2.5
If T = 2.5...
Upstream:
90 = (V-3)(3)
90 = 3V - 9
99 = 3V
33 = V
Downstream:
90 = (V+3)(2.5)
90 = 2.5V + 7.5
82.5 = 2.5V
165 = 5V
33 = V
Since BOTH V's have the same value, this MUST be the solution.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This question can be solved by TESTing THE ANSWERS, but you still have to take lots of notes and stay organized.
First, we have 2 equations that we need to write down (they both involved the Distance Formula and the given 90 mile distance):
Upstream:
90 = (V-3)(T + 1/2)
Downstream:
90 = (V+3)(T)
Since we're multiplying two different sets of values and the product is 90 in both equations, it's highly unlikely that we'll be dealing with a "weird" decimal - we need to end up with round numbers, so the value that I would TEST first is 2.5
If T = 2.5...
Upstream:
90 = (V-3)(3)
90 = 3V - 9
99 = 3V
33 = V
Downstream:
90 = (V+3)(2.5)
90 = 2.5V + 7.5
82.5 = 2.5V
165 = 5V
33 = V
Since BOTH V's have the same value, this MUST be the solution.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
- EricImasogie
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wow thanks guys! its amazing how one needs varying perspectives just to get through some of these problems. I have been so used to doing these s=d/t problems a certain way that I get sidelined when the GMAT throws a problem requiring a different outlook that requires a creative mode of thinking. geesh! thanks guys!
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Hi EricImasogie,
As you continue to study, you're going to find that most GMAT questions can be approached in a variety of ways (they're actually designed that way). Since the Quant section of the GMAT is NOT (strictly speaking) a "math test", you'll benefit greatly by learning other ways of approaching questions beyond "just doing math." You should absolutely continue to post questions in these Forums - you'll learn a lot from everyone here.
GMAT assassins aren't born, they're made,
Rich
As you continue to study, you're going to find that most GMAT questions can be approached in a variety of ways (they're actually designed that way). Since the Quant section of the GMAT is NOT (strictly speaking) a "math test", you'll benefit greatly by learning other ways of approaching questions beyond "just doing math." You should absolutely continue to post questions in these Forums - you'll learn a lot from everyone here.
GMAT assassins aren't born, they're made,
Rich