dear sir/madam
can u plz solve the following word problem by using simultaneous linear equation methods
An aeroplane flies 1680 km with a head wind in 3.5 hours.On the return trip with same wind blowing the plane takes 3 hours.Find the plane's air speed and the wind speed.
Also can u plz explain the meaning of 'head wind' in the above question.
 

Asked by naganshul369 | 11th Jun, 2017, 03:10: PM

Expert Answer:

begin mathsize 16px style Let space the space plane apostrophe straight s space air space speed space be space straight x space km divided by hr space and space the space wind space speed space be space straight y space km divided by hr.
Then comma space speed space of space plane space with space head space wind equals fraction numerator 1680 over denominator 3.5 end fraction km divided by hr equals 480 space km divided by hr
rightwards double arrow straight x minus straight y equals 480 space km divided by hr
rightwards double arrow straight x equals straight y plus 480 space space space space space space space space space space.... left parenthesis straight i right parenthesis
Now comma space speed space of space plane space while space returning equals 1680 over 3 space km divided by hr equals 560 space km divided by hr
rightwards double arrow straight x plus straight y equals 560
Substituting space the space value space of space straight x space from space left parenthesis straight i right parenthesis comma space we space get
straight y plus 480 plus straight y equals 560
rightwards double arrow 2 straight y plus 480 equals 560
rightwards double arrow 2 straight y equals 80
rightwards double arrow straight y equals 40
Substituting space the space value space of space straight y space in space left parenthesis straight i right parenthesis comma space we space get
straight x equals 40 plus 480 equals 520
Thus comma space the space speed space of space air space is space 520 space km divided by hr space and space that space of space wind space is space 40 space km divided by hr.

Note colon
Head space wind space is space the space wind space that space blows space against space the space direction space of space travel space and space tail space wind space
is space the space wind space that space blows space in space the space direction space of space travel.
Speed space of space an space object space increases space with space tailwind space to space reach space the space destination
while space head space wind space decreases space the space speed.
That space is space the space reason space why space aeroplane space took space more space time space while space going space
and space took space less space time space while space returning. end style

Answered by Rashmi Khot | 12th Jun, 2017, 08:47: AM

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