SOLUTION: a cruise ship made a trip of 100 mi in 8 h the ship traveled the first 40 mi at a constant rate before increasing its speed by 5 mph another 60 mi was traveled at the increased spe

Question 1089509: a cruise ship made a trip of 100 mi in 8 h the ship traveled the first 40 mi at a constant rate before increasing its speed by 5 mph another 60 mi was traveled at the increased speed fond the rate of the cruise ship for the first 40 mi?
Found 2 solutions by cjmar, ikleyn:
Answer by cjmar(1)   (Show Source): You can put this solution on YOUR website!
Appreciated.
(Note to admin: I recommend deleting my answer.)
Answer by ikleyn(52773)   (Show Source): You can put this solution on YOUR website!
.
Answer. The rate of the cruise ship for the first 40 mi is 10 miles per hour.

Check.    = 4 + 4 = 8 hours.   ! Correct !

Solution

Let "r" be the slower rate of the cruise ship, in miles per hour. Then the faster speed is (r+5) miles per hour. The time spent to cover 40 miles at the rate "r" mph is hours. The time spent to cover 60 miles at the rate (r+5) mph is hours. The condition says that the total time is 8 hours: + = 8. To solve this equation, multiply both sides by r*(r+5). You will get 40*(r+5) + 60*r = 8r*(r+5). Simplify and solve for "r". 40r + 200 + 60r = 8r^2 + 40r, 8r^2 - 60r - 200 = 0, ====> (divide both sides by 4) ====> 2r^2 - 15r - 50 = 0, = = . Only positive root r= 10 works. Answer. The rate of the cruise ship for the first 40 mi is 10 miles per hour.

Solved.

-------------
-------------
I edited my post.

I apologize for my words in previous version.

RELATED QUESTIONS
A cruise ship made a trip of 140 mi in 8 h. The ship traveled the first 60 mi at a... (answered by lwsshak3)
A ship made a trip of 231 mi in 14 h. The ship traveled the first 98 mi at a constant... (answered by josgarithmetic,ikleyn,MathTherapy)
A ship made a trip of 126 mi in 12 h. The ship traveled the first 48 mi at a constant... (answered by jorel1380)
A ship made a trip of 232 mi in 16 h. The ship traveled the first 96 mi at a constant... (answered by ikleyn)
A cruise ship sailed through a 30-mile inland passageway at a constant rate before its... (answered by Boreal)
A cyclist traveled 60 mi at a constant rate before reducing the speed by 12 mph. Another... (answered by josgarithmetic)
A cyclist traveled 60 mi at a constant rate before reducing the speed by 5 mph. Another... (answered by mananth)
A cyclist traveled 60 mi at a constant rate before reducing the speed by 12 mph. Another... (answered by ikleyn)
Mr. and Mrs. Berg went on a cruise to a tropical island. They spent a total of 26 hours... (answered by ikleyn)