SOLUTION: A cyclist travels 60 km. If he reduces his speed by 2km/h, he will take one hour longer. Find the original speed of the cyclist.

Question 1158453: A cyclist travels 60 km. If he reduces his speed by 2km/h, he will take one hour longer. Find the original speed of the cyclist.
Found 3 solutions by ikleyn, Shin123, MathTherapy:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

            Similar problems were just solved by me SEVERAL times today.

            Therefore, this time I will omit all the words.

The "time" equation is - = 1 hour longer. Solve by reducing to a quadratic equation. Or guess the answer MENTALLY : x = 12 km/h. CHECK. - = - = 6 - 5 = 1 hour. ! Correct !

Solved.

Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
The cyclist originally traveled x km/h. It takes him hours to travel 60 km. If he travels (x-2) km/h, it will take him hours, which is equal to . Multiplying both sides by , we get .
.

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 to standard form by dividing both sides by 1:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is -2, we know that -2=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
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 is equivalent to our original equation .

The highlighted red part must be equal to -120 (highlighted green part).

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (121).

Since the right part 121 is greater than zero, there are two solutions:

, or

Answer: x=12, -10.

A speed can't be negative, so his original speed is 12 km/hr.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A cyclist travels 60 km. If he reduces his speed by 2km/h, he will take one hour longer. Find the original speed of the cyclist.

I hope for your sanity, you didn't look at what the other person presented.
I don't know why some people feel that they can help another person by showing he/she one of the most complex and time-consuming solutions to a math problem.
Is this REALLY help? I think NOT!!
Let original speed, be S
Then his hypothetical speed is S - 2
We then get the following TIME equation:
60(S - 2) = 60S - S(S - 2) ------ Multiplying by LCD, S(S - 2)

(S - 12)(S + 10) = 0
Original speed, or OR S = - 10 (ignore)
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