Source: Economist GMAT
A Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is half the distance between the nest and the lake, what is the average speed, in yards per second, of the bat during the whole flight?
A. 36
B. 40
C. 42
D. 54
E. 65
The OA is D.
A Martian bat flies at 60 yards per second from its nest to
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Hi All,
We're told that a Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is HALF the distance between the nest and the lake, we're asked for the average speed, in yards per second, of the bat during the whole flight. This question can be solved in a couple of different ways. The answer choices are 'spread out' enough that you can actually answer it without doing any math at all though.
Since the two speeds are 60 yards/second and 45 yards/second, we know that the average speed will be some value between those two speeds. There's only one answer that makes sense...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're told that a Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is HALF the distance between the nest and the lake, we're asked for the average speed, in yards per second, of the bat during the whole flight. This question can be solved in a couple of different ways. The answer choices are 'spread out' enough that you can actually answer it without doing any math at all though.
Since the two speeds are 60 yards/second and 45 yards/second, we know that the average speed will be some value between those two speeds. There's only one answer that makes sense...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Rich's approach is definitely the best (i.e., fastest) way to solve this question.BTGmoderatorLU wrote:Source: Economist GMAT
A Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is half the distance between the nest and the lake, what is the average speed, in yards per second, of the bat during the whole flight?
A. 36
B. 40
C. 42
D. 54
E. 65
However, if the answer choices weren't so sweet, here's an algebraic solution
Average speed = (total distance traveled)/(total travel time)
Let's assign nice values to the distances. These values should work nicely with 60 yards per second and 45 yards per second.
So, let's say that 180 yards = the distance from the nest to the lake
This means 90yards = the distance from the lake to the cave
So, TOTAL distance traveled = 180 yards + 90 yards = 270 yards
Since the trip involves 2 legs, we have two different travel times.
We can write: total travel time = travel time during 1st leg + travel time during 2nd leg
time = distance/speed
So, we get: total travel time = 180/60 + 90/45
= 3 + 2
= 5 seconds
So, Average speed = 270 yards/5 seconds = 54 yards per second
Answer: D
Cheers,
Brent
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Let´s solve this problem without taking into account the "examiner´s generosity" (in terms of inviable alternative choices) nor exploring a particular case.BTGmoderatorLU wrote:Source: Economist GMAT
A Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is half the distance between the nest and the lake, what is the average speed, in yards per second, of the bat during the whole flight?
A. 36
B. 40
C. 42
D. 54
E. 65
(Both approaches are important. We just want to avoid repetitions and present the UNITS CONTROL, one of the most powerful tools of our method!)
\[A \to B\,\,:\,\,\,\,\,\left\{ {\,\frac{{60\,\,{\text{yards}}}}{{1\,\,{\text{second}}}}\,\,\,\,\,;\,\,\,\,\,2x\,\,{\text{yards}}} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \to C\,\,:\,\,\,\,\left\{ {\,\frac{{45\,\,{\text{yards}}}}{{1\,\,{\text{second}}}}\,\,\,\,\,;\,\,\,\,\,\,x\,\,{\text{yards}}} \right.\]
\[? = \frac{{{\text{# }}\,\,{\text{total}}\,\,{\text{yards}}}}{{{\text{# }}\,\,{\text{total}}\,\,{\text{seconds}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\,\frac{{2x + x}}{{\frac{{2x \cdot \boxed3}}{{60 \cdot \boxed3}} + \frac{{x \cdot \boxed4}}{{45 \cdot \boxed4}}}}\,\, = \,\,\frac{{3 \cdot x \cdot 18 \cdot 10}}{{10 \cdot x}} = 54\,\,\,\,\left[ {\frac{{{\text{yards}}}}{{{\text{second}}}}} \right]\]
\[\left( * \right)\,\,\,\,\,\frac{{\left[ {\,{\text{yard}}\,} \right]}}{{\,\,\,\left[ {\,\frac{{{\text{yard}}}}{{{\text{second}}}}\,} \right]\,\,\,}} = \,\,\left[ {\,{\text{second}}\,} \right]\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Since we need to calculate average speed, we can use the equation:BTGmoderatorLU wrote:Source: Economist GMAT
A Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is half the distance between the nest and the lake, what is the average speed, in yards per second, of the bat during the whole flight?
A. 36
B. 40
C. 42
D. 54
E. 65
Average speed = total distance/total time
We are given that the Martian bat flies at 60 yards per second from its nest to a dry lake and then immediately continues at 45 yards per second to a nearby cave. We also know that the distance between the lake and the cave is half the distance between the nest and the lake.
We can let d = the distance between the lake and the cave, and so 2d = the distance between the nest and the lake.
Since time = distance/rate:
Time from nest to lake = 2d/60 = d/30
Time from lake to cave = d/45
Finally, we can determine the average speed for the entire trip.
Average speed = total distance/total time
Average speed = (d +2d)/(d/30 + d/45)
Average speed = (3d)/(3d/90 + 2d/90)
Average speed = (3d)/(5d/90)
Average speed = 3/(5/90)
Average speed = 3 x (90/5)
Average speed = 3 x 18
Average speed = 54
Alternate solution:
We can let the distance between the nest and the lake = 180 yards (we choose 180 since it is a multiple of both 60 and 45). Thus, the distance between the lake and the cave = 90 yards. We can now determine the average speed for the entire trip, as follows:
Average speed = total distance/total time
Average speed = (180 + 90)/(180/60 + 90/45)
Average speed = 270/(3 + 2)
Average speed = 270/5
Average speed = 54
Answer: D
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