SOLUTION: Could you please help me with this algebra problem: Sailing time. A boat sails a distance of 440 nautical miles. If the boat had averaged 11 nautical miles more each day, the tri

Question 756789: Could you please help me with this algebra problem:
Sailing time. A boat sails a distance of 440 nautical miles. If the boat had averaged 11 nautical miles more each day, the trip would have required 2 fewer days. How long did the trip take?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A boat sails a distance of 440 nautical miles.
If the boat had averaged 11 nautical miles more each day,
the trip would have required 2 fewer days.
How long did the trip take?
:
Let s = Actual number of miles per day traveled
then
(s+11) = Faster speed of the boat, covering 11 more miles per day
:
Write a time equation: time = dist/speed
:
Actual time - faster time = 2 days
- = 2
Multiply by s(s+11) to cancel the denominators, resulting in:
440(s+11) - 440s = 2s(s+11)
440s + 4840 - 440s = 2s^2 + 22s
Form a quadratic equation on the right
0 = 2s^2 + 22s - 4840
Simplify divide by 2
s^2 + 11s - 2420 = 0
Factors
(s+55)(s-44) = 0
the positive solution
s = 44 miles per day the normal speed
:
How long did the trip take?
= 10 days
:
Check solution using the faster speed (+11 = 55)
= 8 days, 2 less

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