Problem Solving

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

Cheers,
Brent

Hi Joy Shaha,

This is a layered story-problem and takes a lot of effort to solve using a traditional "math approach" (Brent notes it in his explanation: "lots of work here"). Here's how you can solve it with a bit of logic and TESTing THE ANSWERS:

From the prompt, we can create 2 equations:

D = R x T

90 = (V-3)(T + 1/2)
90 = (V+3)(T)

We're asked for the value of T.

From the prompt, I find it interesting that the distance is a nice, round number (90).... because when looking at the answer choices, most of them are NOT nice decimals. When multiplying two values together (as we do in BOTH equations), if you end up with a round number, chances are that either....

1) both numbers are round numbers
2) one of the numbers includess a nice fraction (e.g. 1/2) which can be multiplied and the end result will be a round number.

This gets me thinking that 2.5 is probably the answer, but I still have to prove it....I'm going to plug in THAT value for T and see what happens to the 2 equations....

90 = (V-3)(3)
90 = (V+3)(2.5)

30 = (V-3)
36 = (V+3)

33 = V
33 = V

Notice how both values of V are THE SAME? That means that we have the solution. V=33 and T=2.5

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

A boat traveled upstream a distance of 90 miles at an average speed of
(v-3) miles per hour and then traveled the same distance 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

Since time = distance/rate, the time going upstream = 90/(v - 3) and the time going downstream = 90/(v + 3). Since the time going upstream is ½ hour more than the time going downstream, we can set up an equation as follows:

90/(v - 3) = 90/(v + 3) + 1/2

Let's multiply the equation by 2(v - 3)(v + 3) to get rid of the denominators:

2(90)(v + 3) = 2(90)(v - 3) + (v - 3)(v + 3)

180v + 540 = 180v - 540 + v^2 - 9

540 = v^2 - 549

v^2 = 1089

v = √1089

v = 33

Since the time going downstream = 90/(v + 3), and v = 33, the time going downstream = 90/(33 + 3) = 90/36 = 5/2 = 2.5 hours.

Answer: A