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# A Martian bat flies at 60 yards per second from its nest to a dry lake

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Math Expert
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A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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19 Oct 2016, 23:27
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Difficulty:

25% (medium)

Question Stats:

81% (02:27) correct 19% (02:55) wrong based on 212 sessions

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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

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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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19 Oct 2016, 23:40
1
Distance from nest to lake = d, Speed = 60, Time = d/60

Distance from lake to cave = d/2, Speed = 45, Time = d/90

Average speed = (d + d/2)/(d/60 + d/90) = (3/2)/(1/36) = 54

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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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20 Oct 2016, 09:43
Bunuel wrote:
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 the distance between nest to the dry lake be 180 ( LCM of 60 & 45 )
So, Time taken to reach the dry lake is 3 sec

The distance between the lake to the cave be 90
So, Time taken to reach the cave is 2 sec

Hence Avg speed = $$\frac{270}{5}$$ = $$54$$

So, Answer will be (D) 54

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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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20 Oct 2016, 11:47
Distance Till lake = 2x

Distance from lake to cave = x

Avg speed = 3x/(2x/60+x/45)

=54

Option D
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A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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20 Oct 2016, 16:59
nest - lake = d
lake - cave = d/2

d + d/2/ d/60 + d/2*45
= 3d/2 / d/60 + d/90 = 3d/2 /3d + 2d/180 = 3d/2 / 5d/180 = 3/2 * 180 /5 = 54

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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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20 Oct 2016, 19:10
1
The formula for average speed is
{(p+q(ab))/(qa + pb)}

where the distance is in the ratio p:q and speed of travel in first leg is a, speed in second leg is b.

Substituting the values since distance is in ratio 2:1(p:q)

Avg speed = {3(60)(45)}/{60*1 + 45*2} = 54(Option D)
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A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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02 Nov 2016, 02:56
1
Bunuel wrote:
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

If the bat travels from the Nest to Lake at 60 yards per second and the nest to lake is double the distance from the Lake to the Cave you can use simple ballparking on this question to arrive at the answer.
With ballparking you can immediately remove choices A, B, C, and E by realizing that the bat is traveling a combination of 60 yards per second and 45 yards per second, so you can conclude that the average speed will be both above 45 and below 60. D is the only option.
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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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02 Nov 2016, 04:37
Bunuel wrote:
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

IMO D
Nest<-----------2d--------->Dry lake<----d---->Cave

avg speed= total distance/ total time
avg speed= 3d/{(2d/60)+(d/45)} = 54 yards/second
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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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04 Nov 2016, 09:38
Bunuel wrote:
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 a 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 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

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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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28 Apr 2017, 08:48
1
Knowing that the bat flies at 60 yards per second and 45 yards per second, the average has to be within this range. Looking at the answer choices, we know that the bat never flew slower than 45 yards per second which eliminates answer choices A, B, and C. As we look at answer choice E, we know that the bat never flew faster than 60 yards per second and thus we know the answer is D.
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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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16 Oct 2018, 11:26
Bunuel wrote:
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 particular cases.

(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.
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Re: A Martian bat flies at 60 yards per second from its nest to a dry lake  [#permalink]

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21 Oct 2018, 10:36
The bat flies at a rate of 60 yards/sec for double distance than it travels at a rate of 45 yards/sec. Therefore, the average is going to be closer to 60. Hence, eliminating A, B, C, E, we get the answer 54.
Re: A Martian bat flies at 60 yards per second from its nest to a dry lake   [#permalink] 21 Oct 2018, 10:36
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