1) A light plane flew from its home base to an airport 225 miles away. With a head wind, the trip took 1.7 hrs. The return trip with a tail wind took 1.5 hrs. Find the ave. airspeed of the plane ad the ave windseep.
2) Suppose you bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later, you bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? how much did each party hat cost?
Thank you so much for the help! im just so confused!
1./ Speed X time = distance.....P = plane speed, H = headwind
(P + H)1.7 = 225....divide all by 1.7
P + H = 132.4........equ1
(P - H)1.5 = 225......divide by 1.5
P - H = 150......equ2....now bring down equ 1
P + H = 132.4.....equ1....combine the 2 equations
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2P = 282.4
P = 141.2 MPH
141.2 + H = 132.4
H = 8.8 MPH
Proof
141.2 - 8.8 = 150
150 = 150
2./R = rolls of streamers; H = hats
3R + 15H = 30.....equ1......multiply by 2
6R + 30H = 60......equ1
2R + 4H = 11.......equ2 ......multiply by -3
-6R - 12H = -33.....equ2........now bring up equ1
6R + 30H = 60.......equ1......now combine
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.......18H = 27
H = $1.50.........answer
3R + 15H = 30
3R + 15(1.50) = 30
3R = 7.50
R = $2.50..........answer
Proof
2R + 4H = 11.......equ2
2(2.50) + 4(1.50) = 11
5 + 6 = 11
11 = 11
ave. airspeed of the plane = x
ave wind seep. = y
velocity = distance/times
x-y = 225/1.7
x-y = 132.35....(1)
x+y = 225/1.5
x+y = 150......(2)
add (1) and (2) : 2x = 282.35
x = 141.17 m/s
y = 150-141.17 = 8.83 m/s
2)cost of streamer = x
cost of party hat = y
3x+15y = 30.....(1)
2x+4y = 11........(2)
times (1) with 2/3 : 2x+10y = 20...(3)
(3)-(2) : 6y=9
y = 1.5$
x = 2.5$
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