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A Martian bat flies at 60 yards per second from its nest to

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by BTGmoderatorLU » Mon Oct 15, 2018 2:27 pm

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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.
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by [email protected] » Mon Oct 15, 2018 9:25 pm
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

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Rich
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by Brent@GMATPrepNow » Tue Oct 16, 2018 5:13 am
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
Rich's approach is definitely the best (i.e., fastest) way to solve this question.
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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by fskilnik@GMATH » Tue Oct 16, 2018 10:19 am
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
Let´s solve this problem without taking into account the "examiner´s generosity" (in terms of inviable alternative choices) nor exploring a particular case.

(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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Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Tue Oct 16, 2018 5:15 pm
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
Since we need to calculate average speed, we can use the equation:

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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