Average speed junior drove his rig on interstate 10 from san antonio to el paso. at the halfway point he noticed that he had been averaging 80 mph, while his company requires his average speed to be 60 mph. what must be his speed for the last half of the trip so that he will average 60 mph for the entire trip?

S = d / t
t = d / s
D = half trip distance
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first half (a):
t = d / s
ta = D/80
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second half (b):
t = d / s
tb = D/x
where x is the unknown speed for the second half
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whole trip:
s = d / t
60 = 2D / (ta + tb)
60 = 2D / (D/80 + D/x)
60(D/80 + D/x) = 2D
60(xD/80x + 80D/80x) = 2D
(60D/80x)(x + 80) = 2D
(60/80x)(x + 80) = 2
x + 80 = 2*(80/60)x
x + 80 = (2.666666)x
(2.666666)x - x = 80
(1.666666)x = 80
x = 80/1.666666
x = 48.0
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the speed for the last half of the trip must be: 48 mph

hope this helps