Math help. dont understand linear systems?
Can someone show how to get the answer for the following question
ian flew his airplane at best cruise speed for 2h, then at economy cruise for 3h covering a total of 850km THe next day, he flew at best cruise speed for 3h and economy cruise for 2 h. covering 900km. find the speed for best cruise and economy cruise.
Pls show work and dont be rude.
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ian flew his airplane at best cruise speed for 2h, then at economy cruise for 3h covering a total of 850km
2*B + 3*E = 850
THe next day, he flew at best cruise speed for 3h and economy cruise for 2 h. covering 900km
3*B + 2*E = 900
now multiply through the 1st equation by 3 and the second by 2
6B + 9E = 2250
6B + 4E = 1800
subtract one from the other
5E = 750
E = 150
substitute 150 for E into any of the equations above.
3B + 300 = 900
3B = 600
B = 200
Let best cruise speed be b and economy cruise speed be e,
and use distance = speed * time, to get two equations.
3b + 2e = 900 .............(1)
2b + 3e = 850 ..............(2) subtract (2) from (1)
b - e = 50 .....................(3)
Now add (2) to (1) and divide by 5
b + e = 1750/5 = 350 ....(4).
adding (3) and (4)
2b = 400 so, b = 200
e = b - 50 = 150
Check:
3*200 + 2*150 = 900
2*200 + 3*150 = 850
Regards - Ian
Let x be the speed of airplane @ best cruise in km/hr
Let y be the speed of the airplane @ economy cruise in km/hr
2x+3y=850
3x+2y=900
Eliminate the equations. Multiply each equation by some number to have 1 equal variable.
3(2x+3y)=850(3)
2(3x+2y)=900(2)
New equations
6x+9y=2550
6x+4y=1800
in order to remove one of the variables so the other can be solved, subtract these equations
6x+9y=2550
-(6x+4y=1800)
5y=750
y=150
substitute 150 in any equation
2x+3(150)=850
2x+450=850
x=200
The best cruise's speed is 200 km/hr and economy cruise's speed is 150 km/hr
let x = best cruise speed and y = economy cruise speed
2x + 3y = 850
3x + 2y = 900
So, we can solve this multiple ways. I'll just solve for x in the first equation and substitute it in the second equation.
2x = 850 - 3y
x = (850 - 3y)2
3(850 - 3y)/2 + 2y = 900
solve for y
y = 150
Plug 150 in for y in either equation:
3x + 2(150) = 900
3x + 300 = 900
3x = 600
x = 200
Cruise speed is 200km/h and economy is 150km/h
2b + 3e = 850
3b + 2e = 900
mult eq 2 by 1.5
2b + 3e = 850
4.5b + 3e = 1350
subtract eq 1 from eq 2
2.5b = 500
b = 200 km/hr
e = 150 km/hr