SOLUTION: a boeing 747 flew from san Francisco to Honolulu, a distance of 2900 miles. Flying with the wind, it averaged 600 miles per hour. When the wind changed from tailwind to headwind, t

Question 1084487: a boeing 747 flew from san Francisco to Honolulu, a distance of 2900 miles. Flying with the wind, it averaged 600 miles per hour. When the wind changed from tailwind to headwind, the planes speed dropped to 550 miles per hour. If the total time of the trip was 5 hours, determine the length of the time it flew at each speed
Found 4 solutions by Boreal, josgarithmetic, josmiceli, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
speed in calm air=x
wind speed=w
x+w=600
x-w=550
2x=1150
x=575 mph
t= time with tail wind
5-t= time with head wind
t(600)+(5-t)550=2900
600t+2750-550t=2900
50t=150
t=3 hours at 600 mph (1800 miles)
t=2 hours at 550 mph (1100 miles)
They add to 2900 miles.
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE WITH WIND 600 x 600x AGAINST WIND 550 5-x 550(5-x) TOTALS 5 2900

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Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = time in hrs the plane flew at mi/hr
= time in hrs the plane flew at mi/hr
Let = distance in miles the plane flew at mi/hr
= distance in miles the plane flew at mi/hr
-----------------------------------------------------------
Flying with a tailwind:
(1)
Flying with a headwind:
(2)
--------------------------------
Plug (1) into (2)
(2)
(2)
(2)
(2)
and

----------------------
The plane flew for 3 hrs at 600 mi/hr
The plane flew for 2 hrs at 550 mi/hr
--------------------------------------
check:
(1)
(1)
(1) mi
and
(2)
(2)
(2)
(2) mi
OK

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

a boeing 747 flew from san Francisco to Honolulu, a distance of 2900 miles. Flying with the wind, it averaged 600 miles per hour. When the wind changed from tailwind to headwind, the planes speed dropped to 550 miles per hour. If the total time of the trip was 5 hours, determine the length of the time it flew at each speed

Correct answer:
Ignore all others who say otherwise!!
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