Question

Rational Functions

Create a Model to represent the scenario.

Shrek, Donkey, and Fiona are riding in a carriage to Far Far Away. The horses, Prescott and Thaddeus, are pulling the carriage all the way. Prescott alone could pull the carriage all the way to Far Far Away and back to The Swamp in 21 days, but together they are able to pull the carriage to Far Far Away in 9 days.

Answer 1

Explanation:

Remark

I suppose the question is what is Thaddeus' time to make the trip. This is a fairly common question but not everyone knows how to solve it.

Derivation of the Formula

Prescott + Thaddeus = 1 trip

So the logic of the equation is this.

distance = 1 trip

time = number of dates

rate = ?

rate = distance / time

To find out what the contribution of Thaddeus is set up a distance time formula.

1/21 days is the rate for Prescott

1/x days is the rate for Thaddeus

Together the rate is 1/9

Solution

1/21 + 1/x = 1/9

Subtract 1/21 from both sides

1/x = 1/9 - 1/21

It's not obvious what the LCM is.

9 = 3 * 3

21 = 3 * 7

LCM: 7 * 3 *3 = 63

1/x = 7/63 - 3/63 = 4/63

1/x = 4/63 Cross Multiply

4x = 63 Divide by 4

x = 63/4

Answer

x = 15 3/4

x = 15.75