SOLUTION: A ship made a trip of 232 mi in 16 h. The ship traveled the first 96 mi at a constant rate before increasing its speed by 5 mph. It traveled another 136 mi at the increased speed.
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Question 1142387: A ship made a trip of 232 mi in 16 h. The ship traveled the first 96 mi at a constant rate before increasing its speed by 5 mph. It traveled another 136 mi at the increased speed. Find the rate of the ship for the first 96 mi Answer by ikleyn(52887) (Show Source):
Let x be the rate for the first 96 miles (in miles per hour).
Then the rate for another 136 miles is (x+5) miles per hour, according to the condition.
The time spent for the first 96 miles is hours.
The time spent for the other 136 miles is hours.
The total time equation is
+ = 16 hours.
To solve the equation, first multiply both sides by x*(x+5).
Then simplify and get a quadratic equation in the standard form.
Solve the quadratic equation using the quadratic formula or factoring (choose what works better for you).
The positive root of the quadratic equation will be your answer.
ANSWER. At the end, you should get the rate of 12 miles per hour.
CHECK. + = 8 + 8 = 16 hours. ! Correct !
