GMAT Math

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

I like to begin with a "word equation." We can write:
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

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

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