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

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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(52772)   (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.

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I edited my post.

I apologize for my words in previous version.