SOLUTION: An airplane traveled a distance of 400 km at an average speed of x km/h. Write down an expression for the time taken. On the return journey, the speed increased by 40 km/h. Write d

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Question 540816: An airplane traveled a distance of 400 km at an average speed of x km/h. Write down an expression for the time taken. On the return journey, the speed increased by 40 km/h. Write down an expression for the time for the return journey. If the return journey took 30 minutes less than the outward journey, write down an equation in x and solve it.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
distance = 400
speed = x
t=400/x
speed increased by 40 on return
t= 400/(x+40)
400/x-400/(x+40)=1/2
Lcd = x(x+40)
multiply the equation by the LCD
400(x+40)-400x=x(x+40)/2
400x+16000-400x=(x^2+40x)/2
16000=(x^2+40x)/2
multiply equation by 2
32000 - x^2+40x
x^2+40x-32000=0
x^2+200x-160x-32000=0
x(x+200)-160(x+200)=0
(x+200)(x-160)=0
x= -200 OR 160
neglect negative value
The speed = 160 km/h
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