A canoeist paddled upstream at 10 meters per minute, turned around, an

Question

A canoeist paddled upstream at 10 meters per minute, turned around, and drifted downstream at 15 meters per minute. If the distance traveled in each direction was the same, and the time spent turning the canoe around was negligible, what was the canoeist’s average speed over the course of the journey, in meters per minute?

(A) 11.5
(B) 12
(C) 12.5
(D) 13
(E) 13.5

Kudos for a correct solution.

(A) 11.5
(B) 12
(C) 12.5
(D) 13
(E) 13.5

Kudos for a correct  solution .

KS15 · Accepted Answer

Total distance=d+d=2d
Avg speed=Total distance traveled/Total time taken=2d/(d/10+d/15)=2d/5d/30=12 m/minute
Answer B

HardWorkBeatsAll · Answer

Upstream speed = 10 m/min
Downstream speed = 15 m/min
Let total time travelled in upstream direction = t1
Let total time travelled in downstream direction = t2

Because distance = speed * time, and we know that the distance in both directions was the same, we can write

10 * t1 = 15 * t2

i.e. t1 = 1.5 * t2 (we can also simply find this because times and speeds are inversely proportional. Logically, if it takes X time at 10 m/s, it will take 2/3 X at 15 m/s)

Now, total distance covered = D = D1 + D2 = speed1 * t1 + speed2 * t2

So, D = 10 * t1 + 15 * t2.

In terms of t2,

D = 10 * 1.5 * t2 + 15 * t2 = 30 * t2

Total time taken = T = t1 + t2 = 1.5*t2 + t2 = 2.5 * t2.

So, average speed = D/T = 30*t2 / 2.5*t2 = 12.

Answer is (B) - 12 m/min

HardWorkBeatsAll · Answer

Elegant. +1. I went ahead and wrote a long-winded, boring answer! :oops:

TheKingInTheNorth · Answer

A canoeist paddled upstream at 10 meters per minute, turned around, and drifted downstream at 15 meters per minute. If the distance traveled in each direction was the same, and the time spent turning the canoe around was negligible, what was the canoeist’s average speed over the course of the journey, in meters per minute?

(A) 11.5
(B) 12
(C) 12.5
(D) 13
(E) 13.5

Kudos for a correct solution.

(A) 11.5
(B) 12
(C) 12.5
(D) 13
(E) 13.5

Two speed given - up speed - 10m/min
down speed - 15m/min

let distance be D
Avg speed = total distance/total time = 2D/(D/10)+(D/15) = on solving it = 12 hence B ans .

Bunuel · Answer

KAPLAN OFFICIAL SOLUTION: Step 1: Analyze the Question A canoeist goes one rate in one direction, turns around, and goes back at a different rate. Whenever you deal with one entity that has different rates at different times, set up a chart to track the data. Otherwise, you’ll find yourself in a six-variable, six-equation system that will take a long time to work through. Also, notice that although the distance and time are never mentioned, there are no variables in the answer choices. Whenever variables will cancel out, consider Picking Numbers. Step 2: State the Task Our task is to calculate her average speed for the whole journey. Step 3: Approach Strategically The formula is this: Average Speed = Total Distance / Total Time But we’re seemingly told nothing about time, and the only thing we know about distance is that it is the same in both directions. So what to do? As with almost every problem involving a multistage journey, set up this chart: https://gmatclub.com/forum/download/file.php?id=27817 Now plug in the data we’re given: https://gmatclub.com/forum/download/file.php?id=27818 Now we see clearly that we’ll be able to know the time if we know something about the distance. Since we know whatever variable we put in place will cancel out by the time we get to the answer choices, let’s just pick a number for distance—one that will fit neatly with a rate of 10 and a rate of 15. A distance of 30 should work well: https://gmatclub.com/forum/download/file.php?id=27819 At this point, we can fill in the rest of the chart very straightforwardly. The entire distance is 60. The time taken upstream must be 3, and the time taken downstream must be 2. That makes the entire time 5. https://gmatclub.com/forum/download/file.php?id=27820 Step 4: Confirm Your Answer The speed for the entire trip, then, is 60 / 5 = 12. Answer (B). Reread the question stem, making sure that you didn’t miss anything about the problem. To all of you strategic thinkers out there, can you spot a way to quickly eliminate 3 of the answer choices without doing any calculations? Screen-Shot-2012-06-28-at-1.38.05-PM.png 3.jpg 2-copy.jpg Screen-Shot-2012-06-28-at-1.29.34-PM.png

abani · Answer

When it comes to finding average of two different speed x and y for equal distance, we can use simple formula:
Avg speed = 2xy /x +y

In above question, speeds are 10 m/min and 15 m/min.
Avg speed = (2*10*15)/(10+15) = 300/25 =12

Condon · Answer

I think it is a little easier if you do it like this:

We got 2 equations: (1) Distance= 15 * Time(1)
 (2) Distance= 10 * Time(2)

Now Average Speed formula is Av. Speed= Total ' total distance/total Time'
Total distance= d+d

Total Time= d/15 + d/10

Solving this gives you  2d/5d/30 => 2d*  30/5

So 12 is the answer

Abhishek009 · Answer

Speed upstream is 10 mt/min
Speed down upstream is 15 mt/min

Let the total distance be 30 mt

Time taken to row upstream is 30/10 = 3 min
Time taken to row downstream is 30/15 = 2 min

So, total time taken both ways is 5 min

Total distance travelled is 30+30 =>60 mt

Average speed  =  \frac{Total Distance covered}{Total Time Taken}

Average speed  =  \frac{60}{5}

Average speed  =  12

Hence answer is (B) 12

gracie · Answer

2d=total distance
d/6=total time
2d/(d/6)=12 mph average speed

EMPOWERgmatRichC · Answer

HI All,

This question (and many others just like it) can be solved rather easily by TESTing VALUES. By setting a one-way distance that is a multiple of both 10 and 15, you can do the remaining calculations rather easily (as Abhishek009 showed in his post). Keep an eye out for these opportunities during your practice and on Test Day. Coming up with a simple TEST can help to get to the correct answer without having to do complex work.

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

stevanus.tj · Answer

d1 = d2

distance/speed=time

t1 + t2 = total time

d1/10+ d2/15 = (d1+d2)/average speed

5d/30 = 2d/avg.speed

avg. speed = (2/5) * 30

avg. speed = 12 ( B )

bumpbot · Answer

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