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

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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) About Me  (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) About Me  (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


cross%28600x%2B500%285-x%29=2900%29
highlight_green%28600x%2B550%285-x%29=2900%29

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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs the plane flew at +600+ mi/hr
+5+-+t+ = time in hrs the plane flew at +550+ mi/hr
Let +d+ = distance in miles the plane flew at +600+ mi/hr
+2900+-+d+ = distance in miles the plane flew at +550+ mi/hr
-----------------------------------------------------------
Flying with a tailwind:
(1) +d+=+600t+
Flying with a headwind:
(2) +2900+-+d+=+550%2A%28+5+-+t+%29+
--------------------------------
Plug (1) into (2)
(2) +2900+-+600t+=+550%2A%28+5+-+t+%29+
(2) +2900+-+600t+=+2750+-+550t+
(2) +50t+=+150+
(2) +t+=+3+
and
+5+-+t+=+5+-+3+
+5+-+t+=+2+
----------------------
The plane flew for 3 hrs at 600 mi/hr
The plane flew for 2 hrs at 550 mi/hr
--------------------------------------
check:
(1) +d+=+600t+
(1) +d+=+600%2A3+
(1) +d+=+1800+ mi
and
(2) +2900+-+d+=+550%2A%28+5+-+t+%29+
(2) +2900+-+d+=+550%2A2+
(2) +d+=+2900+-+1100+
(2) +d+=+1800+ mi
OK

Answer by MathTherapy(10552) About Me  (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: 

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