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A bird flies 60 meters at a constant speed from its nest to

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A bird flies 60 meters at a constant speed from its nest to [#permalink]

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A bird flies 60 meters at a constant speed from its nest to a nearby antenna, and continues 80 meters more, flying 5 meters per second faster, to perch on a window pane. The journey from the nest to the antenna takes the bird 4 seconds more than the journey from the antenna to the window pane. The bird flies how many seconds from its nest to the antenna?

A. 5
B. 8
C. 10
D. 12
E. 16
[Reveal] Spoiler: OA

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Re: A bird flies 60 meters at a constant speed from its nest to [#permalink]

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goodyear2013 wrote:
A bird flies 60 meters at a constant speed from its nest to a nearby antenna, and continues 80 meters more, flying 5 meters per second faster, to perch on a window pane. The journey from the nest to the antenna takes the bird 4 seconds more than the journey from the antenna to the window pane. The bird flies how many seconds from its nest to the antenna?

A. 5
B. 8
C. 10
D. 12
E. 16


From nest to antenna: 60 meters, at r meters per second in t seconds --> rt = 60
From antenna to window: 80 meters, at r+5 meters per second in t-4 seconds --> (r+5)(t-4) = 80.

At this point you can plug in options or solve the equations.

Plug in is better.
Start with C: if t=10, then r=60/10=6 --> (r+5)(t-4) = 11*6 = 66, should be 80. Discard.
Try D: if t=12, then r=60/12=5 --> (r+5)(t-4) = 10*8 = 80. Good.

Answer: D.
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Re: A bird flies 60 meters at a constant speed from its nest to [#permalink]

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New post 17 Jul 2014, 02:57
Hi Bunuel,

Thank you for the explanation.

This is an algebra and plug-in combined question.
Is this GMAT style question?

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Re: A bird flies 60 meters at a constant speed from its nest to [#permalink]

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Re: A bird flies 60 meters at a constant speed from its nest to [#permalink]

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New post 17 Jul 2014, 05:32
Thank you for clarification!

Many of the questions I have faced so far could be solved by Algebra only or Plug-in only, or solved by both ways.
And not many of them used the combination of two methods.

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Re: A bird flies 60 meters at a constant speed from its nest to [#permalink]

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New post 01 May 2015, 15:54
Bunuel Now I understand that plugging in numbers is the most efficient way to solve this question.However, while giving the test, I ventured on this journey to try to substitute t or r in one equation or other.I was unable to come to an answer. Would appreciate of you throw some insight. My equations were -

r(t+4)=60
(r+5)t=80

My r and t came out to be fractions and not integers. Wondering what am I doing wrong?

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Re: A bird flies 60 meters at a constant speed from its nest to [#permalink]

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arkle wrote:
Bunuel Now I understand that plugging in numbers is the most efficient way to solve this question.However, while giving the test, I ventured on this journey to try to substitute t or r in one equation or other.I was unable to come to an answer. Would appreciate of you throw some insight. My equations were -

r(t+4)=60
(r+5)t=80

My r and t came out to be fractions and not integers. Wondering what am I doing wrong?


Hi arkle,
Your equations are perfectly fine. I am presuming you made a calculation mistake while solving them. Let me briefly break it down step wise for you.

\(r(t+4)=60\) i.e. \(rt + 4r = 60\)...... Eqn 1
\((r+5)t=80\) i.e. \(rt + 5t = 80\).......Eqn 2

Eqn 1 - Eqn 2 would give us \(5t - 4r = 20\) i.e. \(r = \frac{5t - 20}{4}\)...... Eqn 3

Substituting value of r from Eqn 3 in Eqn 1, we get

\(\frac{5t -20}{4}* (t + 4) = 60\)

\(5t^2 = 320\) i.e. \(t^2 = 64\)

Since \(t\) can't have a negative value, \(t = 8\) seconds which is the time taken by bird to fly from antenna to window pane.

We are asked in the question to find the time taken by bird to fly from nest to antenna i.e. \(t + 4 = 12\) seconds.

Hope its clear

Regards
Harsh
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A bird flies 60 meters at a constant speed from its nest to [#permalink]

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goodyear2013 wrote:
A bird flies 60 meters at a constant speed from its nest to a nearby antenna, and continues 80 meters more, flying 5 meters per second faster, to perch on a window pane. The journey from the nest to the antenna takes the bird 4 seconds more than the journey from the antenna to the window pane. The bird flies how many seconds from its nest to the antenna?

A. 5
B. 8
C. 10
D. 12
E. 16



Let 'S' be the bird's speed from nest to a nearby antenna, then 'S+5' will be speed between Antenna and a window pane.

Given

\(\frac{60}{S} - \frac{80}{(S+5)} = 4\)

\(\frac{15}{S} - \frac{20}{(S+5)} = 1\)

now we can solve the quadratic equation , but we do not need to . In above equation S=5 . 3-2=1.

so answer is \(\frac{60}{5} = 12 Secs\)
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Re: A bird flies 60 meters at a constant speed from its nest to [#permalink]

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New post 04 May 2015, 12:34
Thanks guys.I must have made a calculation mistake.

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goodyear2013 wrote:
A bird flies 60 meters at a constant speed from its nest to a nearby antenna, and continues 80 meters more, flying 5 meters per second faster, to perch on a window pane. The journey from the nest to the antenna takes the bird 4 seconds more than the journey from the antenna to the window pane. The bird flies how many seconds from its nest to the antenna?

A. 5
B. 8
C. 10
D. 12
E. 16


Suppose the speed of the bird from nest to antennae is s.

Then the equation is:

\(\frac{60}{s}\) =\(\frac{80}{s+5}\) +4

The equation becomes

\(s^2\)+10s-75 = 0

(s+15)(s-5) = 0

s = 5 m/sec

Time taken: 60/5 = 12 sec.

D is the answer.

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Re: A bird flies 60 meters at a constant speed from its nest to [#permalink]

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New post 21 Nov 2017, 07:56
arkle wrote:
Now I understand that plugging in numbers is the most efficient way to solve this question.However, while giving the test, I ventured on this journey to try to substitute t or r in one equation or other.I was unable to come to an answer. Would appreciate of you throw some insight. My equations were -

r(t+4)=60
(r+5)t=80

My r and t came out to be fractions and not integers. Wondering what am I doing wrong?


I guess that I know what you did: when you start to substitute (plug in) numbers...you have to remember that the answers must equal t+4 (which is how you expressed the time asked in the stem)... so t+4=12 (t=8 and r=5), in eq. 2 r+5=10 and t=8 multiplied give 80, which confirms the correct answer D.

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Re: A bird flies 60 meters at a constant speed from its nest to   [#permalink] 21 Nov 2017, 07:56
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