Question 756789
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
{{{440/s}}} - {{{440/((s+11))}}} = 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?
{{{440/44}}} = 10 days
:
Check solution using the faster speed (+11 = 55)
{{{440/55}}} = 8 days, 2 less