A boat traveled upstream 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 a half hour longer than the trip downstream, then 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

90/(v-3)=90(v+3)+.5

90[v+3-v+3]/(v*v-9)=.5
90*6/(v*v-9)=.5
90*12+9=v*v
v*v=1089
v=33
v+3=36

Time required to travel downstream=90/36=2.5 hours

Upstream time = downstream time + 0.5

90/(v-3) = 90/(v+3) + 1/2
90 (1/(v-3) - 1/(v+3))= 1/2
90 (6/(v^2-9)) = 1/2
v^2 = 1089
V = 33

Downstream time = 90/36 = 2.5

Answer is (a)
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solve the below equation to reach upon speed of boat-

90/(v+3) - 90/(v-3) = 1/2
V=33

therefore time required while travelling downstream- 90/(33+3) = 90/36 = 2.5

Answer:- A

Let me take your question first:

It is a good idea to remember squares of numbers till 20. They come in handy sometimes.
To find the square root of bigger numbers (which are perfect squares), observe the following:
1. A square of a number only ends in 0/1/4/5/6/9.
-If it ends in 0, it will have even number of 0s at the end and the square root will end in 0 (I know 1340 cannot be a perfect square.)
-If it ends in 1, the square root will end in 1/9 (e.g. root 361 = 1[highlight]9[/highlight], root 441 = 2[highlight]1[/highlight])
-If it ends in 4, the square root will end in 2/8
-If it ends in 5, there will be a 2 right before it and its square root will end in 5 (e.g. root 625 = 25, root 675 is not an integer)
-If it ends in 6, the square root will end in 4/6.
-If it ends in 9, the square root will end in 3/7.
These are all derived by just observing the last digits when we square a number.. You don't need to learn this.

Since 1089 ends in a 9, its square root will end in 3/7.
Also 30^2 = 900 so root of 1089 will be greater than 30.
But 40^2 = 1600 so root of 1089 will be much less than 40. The number that can be the square root of 1089 is 33 (if 1089 is a perfect square). You can square 33 to check.

Also, an equation like \frac{90}{{v -3}} - \frac{90}{{v + 3}} = \frac{1}{2}, doesnt need to be solved.

99% chance is that v will be an integer.
The options give me values for \frac{90}{{v + 3}}

Let me say if it is 2.5, then 90/2.5 = 36 and v = 33
Then \frac{90}{{v - 3}} = 3. I get the difference of 1/2 an hour. 2.5 satisfies my condition.

Had 2.5 not been the first option, you might say that it would take me a long time to check each option.
No. 90/2.4 = 900/24 which is not an integer since 900 is not divisible by 8 so it will not be divisible by 24
90/2.3. No ways 900 is divisible by 23
90/2.2. No ways 900 is divisible by 11
90/2.1. No ways 900 is divisible by 7
In fact, when I look at the options, the first one I try is 2.5. With practice, you will gain the instinct.
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90/(v-3) = 90/(v+3) + 1/2

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

=> 90 * 6 * 2 = v^2 - 9

=> v^2 = 1080 + 9

=> v^2 = 9 (120 + 1)

=> v^2 = 3^2 * 11^2

=> v = 3*11 = 33

So Downstream time = 90/36 = 30/12 = 2.5 hrs

Answer - A
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Can someone pls help with the above question? What is the most efficient way to do this. Here's what i've got..

If one takes the time for the trip downstream to to be T, then one gets
UPSTREAM:
V-3 = 90 / (T + 1/2)

DOWNSTREAM
V+3 = 90 / T

Now no matter how much I simplify I end up with a complicated equation, and then it will be plugging in off answer choices but that takes >3 minutes at least.
Any suggestions for a sohrtcut, I'm sure there's an easy way..
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A boat traveled upstream a distance of 90miles at an average speed of (v-3) miles per hour and then traveled down stream at an average of (v+3) miles per hour. If upstream look 30 min more than downstream time, how much time did the boat travel downstream?
a) 2.5
b) 2.4
c) 2.3
d) 2.2
e) 2.1

how to solve these kind of questions in 2 min? any short way...
\frac{90}{(v-3)}=\frac{90}{(v+3)} +1/2
solving for v, value of \frac{90}{(v+3)} is tedious... and answer choices are in too close range to make an estimation.... how should I be tackling these?

Hi guys,

I am having difficulties with this one:
A boat travelled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then travelled the same distance downstream at an average speed of (v+3) miles per hour. If the upstream trip took half an hour longer than the downstream trip, how many hours did take the boat to travel downstream?

a) 2.5
b) 2.4
c) 2.3
d) 2.2
e) 2.1

Thanks a lot for your help!

It needs practice. You need to believe that you can solve the question very quickly for you to be able to think up of logical approaches. In GMAT, you can solve almost every question within two minutes so if you get a big complicated equation, you can be sure that you are missing something. If the question looks really complicated, we know there has to be a trick (In fact, one tends to overlook the so called short-cuts when questions are simple and don't take much time anyway).
I would suggest you to read up and practice the logical solutions - once you understand the logic, try using it in other questions. Don't worry about the time factor. I discuss some logic based ideas regularly on my blog. Check it out:

http://www.veritasprep.com/blog/categor ... om/page/3/
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Karishma
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