Question 1203688
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x = number of hours since 12:00 pm noon


Cargo Plane
distance = rate*time
d = r*t
d = 180x


Jet Aircraft
d = r*t
d = 450(x-1)
The x-1 refers to the fact the jet is in the air 1 hour less compared to the cargo plane. 


The jet will pass the cargo plane when the two distances are equal.
450(x-1) = 180x
450x-450 = 180x
450x-180x = 450
270x = 450
x = 450/270
x = (5*90)/(3*90)
x = 5/3
x = (1+2)/3
x = (1/3) + (2/3)
x = 1 + (2/3)
x = 1 & 2/3


1 & 2/3 hr = 1 hr + (2/3) hr
1 & 2/3 hr = 1 hr + (2/3)*60 min
1 & 2/3 hr = 1 hr + 40 min


The jet will overtake the cargo plane 1 hour and 40 minutes after the cargo plane takes off.


Add this duration to 12:00 pm noon to get
12:00 + 1:40 = <font color=red size=4>1:40 pm</font> which is the final answer.
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