A crew can row a certain course up the stream in 84 minutes; they can

Question

A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 9 minutes less than they can row it in still water. How long would they take to row down with the stream

A. 45 or 23 minutes
B. 63 or 12 minutes
C. 60 minutes
D. 19 minutes
E. 25 minutes

A. 45 or 23 minutes
B. 63 or 12 minutes
C. 60 minutes
D. 19 minutes
E. 25 minutes

pradeep15793 · Accepted Answer

let r=rowing speed
c=current speed
1=distance
Speed for rowing upstream is (r-c) as u have to row against the water current
Speed for rowing downstream is (r+c) as u row along the current
Speed for rowing in still water will be just r

Time taken for rowing upstream is 84 min
1=(r-c)*84
Let t=downstream time
1=(r+c)*t
Question says that they can row the same course down stream in 9 minutes less than they can row it in still water
So time taken for rowing in still water will be (t+9)
1=r*(t+9)

Restating above 3 questions as
r-c = 1/84
r+c = 1/t
r = 1/(t+9)
Adding statements 1 & 2 gives
2r = 1/84 + 1/t
Substituting r = 1/(t+9) in above
2/(t+9) = 1/84 + 1/t
Rearranging terms will form
t^2-75t+756=0
By solving, t= 12 or 63

Kudos please if helped

Posted from my mobile device

subhashghosh · Answer

This did not seem to be an OG problem, so I searched and found the following :

https://www.urch.com/forums/gmat-problem ... tream.html

@ramkryp, please quote the source correctly while posting the problems.

ramkryp · Answer

@ Subash, I am sorry, I am new here.

gracie · Answer

let r=rowing speed
c=current speed
t=downstream time
1=distance
r+c=1/t
r-c=1/84
adding, 2r=1/t+1/84
r=1/(t+9)
thus, (1/t+1/84)/2=1/(t+9)
➡t^2-75t+756=0
(t-63)(t-12)=0
t=63 or 12 minutes
B

jibberjabber · Answer

Could someone explain the process again? Thanks

prashanths · Answer

Not quite sure why we would have two answers. The time taken to go upstream and downstream should be almost equidistant from the time taken to go in still water.

Which would eliminate 12 and the answer would be 63 only?

Fdambro294 · Answer

The Cases of:

When a Boat is Traveling WITH the current downstream = Speed of Boat + Speed of Current

When a Boat is Traveling in STILL WATER = Speed of Boat

When a Boat is Traveling AGAINST the current upstream = Speed of Boat - Speed of Current

these 3 Cases of Speeds are in Arithmetic Progression. Since the Distance in all 3 Cases is the Same/Constant, Speed is Inversely Proportional to Time.

Thus, since the 3 Speeds are in Arithmetic Progression, the TIME it takes in each case will be in Harmonic Progression and you can find the Harmonic Mean = Time it takes rowing in Still water with NO Current.

Let Speed of Boat = R
Let Speed of Current = C
Let Time it takes to travel Downstream WITH the Current = T

Traveling Downstream Speed = R + C
Traveling with NO Current in Still Water Speed = R
Traveling AGAINST the Current Upstream Speed = R - C

As you can see: —R+C , R , R - C — :are in Arithmetic Progression. Over the Same Distance of the lake, the Time it takes traveling at each Speed will be in Harmonic Progression. The Harmonic Mean of the Times can then be found to solve for the Time it takes to travel the distance in Still Water with NO Current.

Time taken to Travel with the current Downstream = T

Time taken to Travel in Still Water = T + 9

Time taken to Travel AGAINST the Current Upstream = 84 minutes

Since these Times are in Harmonic Progression, we can found the Harmonic Mean of the 3 Times, which = T + 9

Harmonic Mean of 3 numbers in HP = b (middle number in HP) = (2 * a * c) / (a + c)

T + 9 = 2 * (T) * (84) / T + 84

After performing the Algebra, you end up with a Quadratic Equation:

(T)^2 - 75*T + 756 = 0

Solving for the Quadratic, you see why 2 Root Answers are Possible. The C Value is (+)Positive and the Middle B Value is (-)Negative. You will have 2 Binomials with subtraction in them and end up with 2 Possible Valid Solutions

(T - 12) * (T - 63) = 0

T can = 12 minutes or 63 minutes

Edit: I believe the post above me is right. 12 minutes could not be the answer, leaving only 63 min as the only solution.

useradm · Answer

Is there any easy method to solve these kinda quadratic equations it seems a bit difficult because of the big numbers and may take too much time  mikemcgarry   Bunuel

Stella5200 · Answer

Took a while for me to wrap my head around around.. what helped was the concept that since upstream and downstream have the same number of variables in different direction they can cancel out to 2S1 = D/84 + D/t and S1 is nothing but D/x so across the numerator D cancels out...

When you come down to the quadratic.. I struggled with trying to solve for root when in reality the sum of the roots have to sum to 75... so simply look at the options and see which of them sum to 75 which is only Option B (63 + 12 =75)

Little tricks I found that simplified the problem and saved time.

A crew can row a certain course up the stream in 84 minutes; they can

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A crew can row a certain course up the stream in 84 minutes; they can

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