SOLUTION: After sailing 15 miles a boat changed direction and increased speed by 2 mph. At this 2 mile faster speed an additional 19 miles was traveled. The total travel time was 4 hours. W

Question 522971: After sailing 15 miles a boat changed direction and increased speed by 2 mph. At this 2 mile faster speed an additional 19 miles was traveled. The total travel time was 4 hours. What is the rate of the boat for the 1st 15 miles?
Thank you in advance.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
After sailing 15 miles a boat changed direction and increased speed by 2 mph. At this 2 mile faster speed an additional 19 miles was traveled. The total travel time was 4 hours. What is the rate of the boat for the 1st 15 miles?
**
let x=rate of speed of boat for 1st 15 miles of travel
x+2=rate of speed of boat for additional 19 miles of travel
Travel time=distance/speed
..
(15/x)+(19/(x+2))=4
LCD:x(x+2)
15(x+2)+19x=4x(x+2)
15x+30+19x=4x^2+8x
4x^2-26x-30=0
2x^2-13x-15=0
(2x-15)(x+1)
2x-15=0
x=15/2=7.5
or
x+1=0
x=-1 (reject, speed>0)
ans:
rate of speed of boat for 1st 15 miles of travel=7.5 mph
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