SOLUTION: A cruise ship made a trip of 140 mi in 8 h. The ship traveled the first 60 mi at a constant rate before increasing its speed by 5 mph. Then it traveled another 80 mi at the increas

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Question 597471: A cruise ship made a trip of 140 mi in 8 h. The ship traveled the first 60 mi at a constant rate before increasing its speed by 5 mph. Then it traveled another 80 mi at the increased speed. Find the rate of the cruise ship for the first 60 mi.
Answer by lwsshak3(11628) About Me  (Show Source):
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A cruise ship made a trip of 140 mi in 8 h. The ship traveled the first 60 mi at a constant rate before increasing its speed by 5 mph. Then it traveled another 80 mi at the increased speed. Find the rate of the cruise ship for the first 60 mi.
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let x=rate of speed for first 60 mi
(x+5)=rate of speed for remaining 80 mi
travel time=distance/speed
..
60/x+80/(x+5)=8
LCD: x(x+5)
60(x+5)+80x=8x(x+5)
60x+300+80x=8x^2+40x
8x^2-100x-300=0
divide by 4
2x^2-25x-75=0
(2x+5)(x-15)=0
2x+5=0
x=-5/2 (reject, x>0)
x-15=0
x=15
ans:
rate of speed of the cruise ship for first 60 mi=15 mph