if the speed of an aeroplane is decreased by 120km/h ,it takes 18 minutes more to travel some distance . if the speed is increased by 180km /h, it takes 18 min less to travel the same distance . find the average speed of the aeroplane and the distance
Answers
distance of aeroplane is 1080km
Step-by-step explanation:
let speed be x km / hr
time be y hr
distance covered is same given
distance = speed × time
d = x×y — (1)
from (1) condition
(x-120) (y+18/60) = xy
(x-120) (y+0.3) = xy
xy + 0.3x - 120y - 36 = xy
xy will get cancelled
Hence, Multiply the equation by 10
3x - 1200y = 360 —(2)
from second condition
(x+180) (y-0.3) = xy
xy - 0.3x + 180y - 54 = xy
xy will get cancelled
Hence, Multiply the equation by 10
-3x + 1800y = 540
3x - 1800y = -540—(3)
Subtract equation second from third
3x - 1800y = -540
- 3x - 1200y = 360
- + -
——————————
- 600y = -900
y = 900/600 = 3/2
from (1) equation,
d = xy
d = (x - 120) ( 3/2 + 0.3)
= 1.8x-216 — (4)
d is same — from given
d = (x + 180) (1.2)
d = 1.2x + 216 — (5)
from (4) and (5)
1.8x- 216 = 1.2 + 216
1.8 - 1.2x = 216 +219
0.6x = 432
6x = 4320
x = 4320/6
x = 720km/hr — (6)
Put x = 720 in equation (4)
d = 1.8 (720) - 216
d = 1296 - 216
d = 1080km
The distance of aeroplane is 1080km.