Week 15/ Rational Equation’s in Word Problems

Starting off with word problems you also want to read the equation a few times over and underline any important words that with give you an idea of what kind of a word problem you’ll be solving.

Given a word problem underline key words: Jorge rows a boat 24km down stream and back where they began. When the average speed of the current is 2km/h, they can complete the journey in 9 hours. What is Jorge’s average rowing speed in still water.

(Note: If in the word problem you find the word from at any time, reverse the two fractions/ or numbers.)

A key thing to help you solve these equtions is D = S x T, which means Distance = Speed times Time formula.

In the word problem (Jorge rows a boat 24km down stream and back where they began. When the average speed of the current is 2km/h, they can complete the journey in 9 hours. What is Jorge’s average rowing speed in still water.)

We pulled out key words in the sentence that will give us a clue to what will be solved the 24km down stream represents that the equation D S = T. And if you fill in the numbers it would have 24km as the distance. The sentence (Back where they began also tells us its for both fractions. So 24 will be the distance all around both up and down stream. Now we need the speed to divide the distance by. In the sentence (average speed of the current is 2km/h) we know that x+2 must be the speed going downstream and x-2 is the speed going up. Because if you think about it going up stream your going against the current and going down the current is pushing you by you overall speed. So now the equation is + = ?. We still are missing the time it took, but luckily in the sentence we underlined (they can complete the journey in 9 hours.) Meaning that the total time it took is nine hours completing the equation D S = T now we just need to solve for x.  + = 9

You can do multiple things with this equation but what I would recommend is doing is common denomonator, and dont forget to right down you non-permissible values which is + or – 2. Then just factor.

The reason why I crossed out -2/3 is because it is a negitive number and the speed connnot be a negitive number.