SOLUTION: A cruise ship sailed through a 30-mile inland passageway at a constant rate before its speed was increased by 25 mph. Another 90 mi was traveled at the increased rate. The total ti

Question 1107744: A cruise ship sailed through a 30-mile inland passageway at a constant rate before its speed was increased by 25 mph. Another 90 mi was traveled at the increased rate. The total time for the 120-mile trip was 3 h. Find the rate of the ship during the last 90 mi.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
constant speed was x mph
x*t1=distance
t1=30/x for the first part
x+25 was second speed
t2=90/(x+25) is time for the second part
t1+t2= 3
(30/x)+(90/(x+25))=3
Multiply by x(x+25) both sides
30x+750+90x=3x^2+75x
collect terms
3x^2-45x-750=0
3(x^2-15x-250)=0
(x-25)(x+10)=0
use positive root only x=25 mph speed first part
50 mph for second part ANSWER
Took 30/25=1.2 hours to navigate the first part
90/50 or 1.8 hours to navigate the second part
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