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

Question

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

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

Bunuel · Accepted Answer

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.

ManyataM · Answer

IMO the answer is option B

I dont know but this took me more than 2 mins to solve. I am looking for others to post so that I could find a better and faster approach to this question

rvgmat12 · Answer

Answer must be D
Backsolving is better approach for this imo

D - 12 sec
60/12 = 5 m/s
80/(5+5) = 8 sec

Difference = 4 sec - given

hykhan · Answer

The answer is D.

You can use a hybrid approach of building an equation and plugging numbers if you don't want to go through the whole quadratic equation.

Rate of bird * Time = Distance

1) r*t = 60m

In the second part, the bird flys 5 m/s faster, and saves 4 seconds in time while covering 80m.

2) Second equation --> (r+5)(t-4) = 80

At this point, you need to be smart with plugging numbers. Choose a value of 5 as your starting rate because its an easy number to work with.

If the bird moved at a speed of 5 m/s initially, it would take 12 seconds to cover 60m. By that logic, in the second equation adding 5 m/s to a rate of 5 m/s gives you 10 m/s. Subtracting 4 seconds from 12 (the initial time) gives you a value of 8 seconds, and what do you know, that equals 80!

Therefore, the time it takes the bird to go from the nest to the antenna is (D) 12 seconds.

This approach shouldn't take you more than 1-2 minutes if you're smart about the numbers you pick, but if you would much rather be sure and you are fast with equations then you can fill out the entire quadratic and you'll get

rt=60
(r+5)(t-4) = 80
rt + 5t -4r - 20 = 80
60 + 5(60/r) - 4r - 20 = 80
300/r - 4r = 40
300 - 4r^2 -40r = 0
r^2 + 10r - 75 = 0
(r+15)(r-5) = 0

Since r can't be a negative, r must be 5. Therefore rt = 60, t = 60/r = 12.

ManyataM · Answer

I did with the same approach only.. But took 2.30 mins

Posted from my mobile device

MathRevolution · Answer

Nest to Antenna: Distance is 60 and time let's says is 12

Speed:  \frac{60 }{ 12}  = 5 mpsec

Antenna to pane: Distance is 80 and speed will be 5 + 5 = 10 and hence time taken:  \frac{80 }{ 10}  = 8 sec.

Difference in time= 12 - 8 = 4

Answer D

Nirmesh83 · Answer

MathRevolution   VeritasKarishma  Solving the problem by options is best method in this question. Please describe actual process of solving the question.

KarishmaB · Answer

Say time taken to fly from nest to Antenna is T secs.

Speed from nest to Antenna + 5 = Speed from Antenna to Window

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

I would plug in the options at this point and the first option I will try is 12 because (T - 4) denominator on the RHS should be such that it is a factor of 80 and I will look for some middle value. It works.
It is easy to plug in values when your variable is in the denominator in such equations. Very few values work to give you integers which are usually what the solution demands. Hence, one arrives at the answer very quickly.

Answer (D)

If you do not want to use the options,

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

(60 + 5T)(T - 4) = 80T 
 T^2 - 8T - 48 = 0 
T = 12 or -4

Nirmesh83

Nirmesh83 · Answer

Thanks

bumpbot · Answer

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

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