Against the wind a plane travels 5600 km in 7hrs. With wind the plane travels 8160 km in 8 hrs. rate in still air and rate of wind?
回答 (7)
2017-07-16 12:33 am
Let p km/hr be the rate of the plane in still air, and w km/hr be the rate of the wind.
Rate of the plane in km/hr when traveling against the wind :
p - w = 5600/7
Hence, p - w = 800 …… [1]
Rate of the plane in km/hr when traveling with wind :
p + w = 8160/8
Hence, p + w = 1020 …… [2]
[1] + [2] :
2p = 1820
p = 910
[2] - [1] :
2w = 220
w = 110
The rate of the plane in still air = 910 km/hr
The rate of the wind = 110 km/hr
Rate of the plane in km/hr when traveling against the wind :
p - w = 5600/7
Hence, p - w = 800 …… [1]
Rate of the plane in km/hr when traveling with wind :
p + w = 8160/8
Hence, p + w = 1020 …… [2]
[1] + [2] :
2p = 1820
p = 910
[2] - [1] :
2w = 220
w = 110
The rate of the plane in still air = 910 km/hr
The rate of the wind = 110 km/hr
2017-07-16 1:11 am
v + w = 8160/8 = 1020
v - w = 5600/7 = 800
2v = 1820 so plane spped in still air is 910 km/h
2w = 220, so wind speed is 110 km/h
This works for questions about boats up and down stream as well.
v - w = 5600/7 = 800
2v = 1820 so plane spped in still air is 910 km/h
2w = 220, so wind speed is 110 km/h
This works for questions about boats up and down stream as well.
2017-07-16 12:25 am
Rate with wind is 1020 km/h, rate against wind is 800 km/h.
vp + vw = 1020, vp - vw = 800 =>
2vp = 1820 =>
speed of plane in still air is 910 km/h,
and the speed of the wind is 110 km/h.
vp + vw = 1020, vp - vw = 800 =>
2vp = 1820 =>
speed of plane in still air is 910 km/h,
and the speed of the wind is 110 km/h.
2017-07-16 3:55 am
w and p are the speeds of the wind and plane, respectively.
Going against the wind, the plane travels (p-w) km per hour.
5,600 km/(7 h) = 800 km/h
p-w = 800
Going with the wind, the plane travels (p+w) km per hour.
8,160 km/(8 h) = 1,020 km/h
p+w = 1,020
p-w = 800
p+w = 1,020
--------------
2p = 1,820
p = 910 km/h
w = 1,020-p = 110 km/h
Going against the wind, the plane travels (p-w) km per hour.
5,600 km/(7 h) = 800 km/h
p-w = 800
Going with the wind, the plane travels (p+w) km per hour.
8,160 km/(8 h) = 1,020 km/h
p+w = 1,020
p-w = 800
p+w = 1,020
--------------
2p = 1,820
p = 910 km/h
w = 1,020-p = 110 km/h
2017-07-16 1:58 am
Let rate in still air = x mph
Let wind speed = w mph
7 [ x - w ] = 5600
8 [ x + w ] = 8160
7x - 7w = 5600
8x + 8w = 8160
x - w = 800
x + w = 1020______add
2x = 1820
x = 910 mph______rate in still air
w = 110 mph_____wind speed
Let wind speed = w mph
7 [ x - w ] = 5600
8 [ x + w ] = 8160
7x - 7w = 5600
8x + 8w = 8160
x - w = 800
x + w = 1020______add
2x = 1820
x = 910 mph______rate in still air
w = 110 mph_____wind speed
2017-07-16 1:12 am
Let x be te speed of the plane
Let w be the rate of wind
distance /time = speed
5600 / 7 = x-w
7x-7w = 5600 -----(1)
8160/8 = x+ w
8x+8w = 8160 -----(2)
multiply equation (1) by 8 and equation (2) by 7
56x-56w = 44800
56x-56w = 57120
add:
112 x = 101920
x= 101920 /112 = 910 mph (speed of the plane)
7x-7w = 5600 -----(1)
7(910) - 7 w = 5600
-7w = 5600 - 7(910)
-7w = 5600 -6370
-7w = -770
w = 110 mph (speed of wind)
Let w be the rate of wind
distance /time = speed
5600 / 7 = x-w
7x-7w = 5600 -----(1)
8160/8 = x+ w
8x+8w = 8160 -----(2)
multiply equation (1) by 8 and equation (2) by 7
56x-56w = 44800
56x-56w = 57120
add:
112 x = 101920
x= 101920 /112 = 910 mph (speed of the plane)
7x-7w = 5600 -----(1)
7(910) - 7 w = 5600
-7w = 5600 - 7(910)
-7w = 5600 -6370
-7w = -770
w = 110 mph (speed of wind)
2017-07-16 12:30 am
let w = rate of wind
let v = rate of plane
d = vt
7(v - w) = 5600
8(v + w) = 8160
v - w = 800
v + w = 1020
2v = 1820
v = 910 km/hr => rate of plane
w = 1020 - 910 = 110 km/hr => rate of wind
I hope this helps.
let v = rate of plane
d = vt
7(v - w) = 5600
8(v + w) = 8160
v - w = 800
v + w = 1020
2v = 1820
v = 910 km/hr => rate of plane
w = 1020 - 910 = 110 km/hr => rate of wind
I hope this helps.
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