SOLUTION: At noon, a cargo plane leaves Angama airport and heads towards Bamburi 500 km away at 180 km/h. At 1.00 pm, a jet takes off from Angama and flies on the same course at 450 km/h. Wh

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Question 1203688: At noon, a cargo plane leaves Angama airport and heads towards Bamburi 500 km away at 180 km/h. At 1.00 pm, a jet takes off from Angama and flies on the same course at 450 km/h. What time will the jet overtake the cargo plane?
Found 2 solutions by math_tutor2020, mananth:
Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!

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 = 1:40 pm which is the final answer.

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
At noon, a cargo plane leaves Angama airport and heads towards Bamburi 500 km away at 180 km/h.
At 1.00pm the plane has traveled 180 kms
At 1.00 pm, a jet takes off from Angama and flies on the same course at 450 km/h.
The distance to overtake is 180 kms
The effective speed = 450-180 = 270 km/h ( Since both are flying in the same durection)
Time = distance /speed
=180/270= 2/3 hour
The jet overtakes the cargo plane after 40 minutes

What time will the jet overtake the cargo plane?
The jet will overtake the cargo plane at 1:40 pm.