| Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics |
| Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square. Let's convert We have: Look at We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that The highlighted red part must be equal to -25 (highlighted green part). So, the equation converts to Our equation converted to a square Since the right part 25.25 is greater than zero, there are two solutions: , or Answer: x=5.52493781056044, -4.52493781056044. |
Let x be the spreed of the boat in still water, in kilometres per hour.. Then the speed downstream is (x+5) kilometres per hour, and the time traveled downstream ishours. The speed upstream is (x-5) miles per hour, and the time traveled upstream is hours. The total time equation is + = 4 Cancel the factor 2 in both sides + = 2 Multiply both sides by (x+5)*(x-5); then simplify (x-5) + (x+5) = 2*(x^2-25) 2x = 2x^2 - 50 2x^2 - 2x - 50 = 0 x^2 - x - 25 = 0 = = = . Only positive root x = = 5.525 is the solution. ANSWER. The speed of the boat in still water is 5.525 kilometres per hour. CHECK. + = 4 hours. ! Correct !