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Once a certain airplane attains its maximum speed of 300 miles per hou

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Bunuel
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Once a certain airplane attains its maximum speed of 300 miles per hou [#permalink] New post   14 Dec 2020, 03:30
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Once a certain airplane attains its maximum speed of 300 miles per hour (mph), it begins decreasing speed as it approaches its destination. After every 50 miles, the plane decreases its airspeed by 20 mph. Which of the following equations best defines the number of miles the plane has traveled (m) after beginning to decrease speed as a function of the airplane’s airspeed (s)?


A. s = -5m/2 + 750

B. s = -2m/5 + 300

C. m = -5s/2 + 750

D. m = -5s/2 + 300

E. m = 2s/5 + 300
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Re: Once a certain airplane attains its maximum speed of 300 miles per hou [#permalink] New post   14 Dec 2020, 05:24
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Once a certain airplane attains its maximum speed of 300 miles per hour (mph), it begins decreasing speed as it approaches its destination. After every 50 miles, the plane decreases its airspeed by 20 mph. Which of the following equations best defines the number of miles the plane has traveled (m) after beginning to decrease speed as a function of the airplane’s airspeed (s)?


A. s = -5m/2 + 750

B. s = -2m/5 + 300

C. s = -5s/2 + 750

D. s = -5s/2 + 300

E. s = 2s/5 + 300


Every 50 miles decrease = 20 miles/hr decrease in speed
=> Every 1 miles decrease = \(\frac{20}{50}\) miles/hr decrease in speed
=> Every "m" miles decrease = \(\frac{2}{5}\)m decrease in speed
This decrease is shown as -ve, so, -\(\frac{2}{5}\)m

If "m" is the miles and "s" is the speed, so decrease in speed after attaining the maximum speed of 300 is given by

s = 300 - \(\frac{2}{5}\)m

(B)
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Re: Once a certain airplane attains its maximum speed of 300 miles per hou [#permalink] New post   19 Dec 2020, 23:55
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Max Speed = 300 MPH
Speed reduces by 20 MPH after every 50 Miles. This means that in order for the plane to lose all its speed, the plane has to travel 750 miles.
750 is arrived at by considering the fact that in order for the plane to lose all 300 MPH of speed, it would need 15 intervals of 20 MPH speed losses (300/20). Since the plane needs 15 intervals to lose all the speed, it will have to travel 15 stretches of 50 Miles. Therefore, 750 = 15*50 or 300/20*50

Based on the above, the function can be arrived as m = 750 - (50/20)s
m = 750 - (5/2)s (Option C)
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Re: Once a certain airplane attains its maximum speed of 300 miles per hou [#permalink] New post   28 Dec 2020, 07:16
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Wsd65798 wrote:
Max Speed = 300 MPH
Speed reduces by 20 MPH after every 50 Miles. This means that in order for the plane to lose all its speed, the plane has to travel 750 miles.
750 is arrived at by considering the fact that in order for the plane to lose all 300 MPH of speed, it would need 15 intervals of 20 MPH speed losses (300/20). Since the plane needs 15 intervals to lose all the speed, it will have to travel 15 stretches of 50 Miles. Therefore, 750 = 15*50 or 300/20*50

Based on the above, the function can be arrived as m = 750 - (50/20)s
m = 750 - (5/2)s (Option C)


Hi Wsd65798,
Thank you for your solution , but what you have arrived at is option B and NOT option C.
Simplifying your equation in terms of s we would get :
\(\frac{5}{2}s=-m+750\)
Simplifying further we get =\( \frac{-2}{5}m+300\) (Option B )

So to verify that option B is correct :
Let current Speed be 300
Then after 50 miles it's speed should be 280 (reduced by 20 )
putting m=50 in option B we get S=280

Bunuel IMO option B should be the OA.
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Re: Once a certain airplane attains its maximum speed of 300 miles per hou [#permalink]
28 Dec 2020, 07:16
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