Overview
Week 8 Discussion – Rational Expressions in Real Life
This week, you will learn about rational expressions. While the term “rational expression” might sound very mathy, it does have some pretty neat usage in the real world. Watch this video to learn one such application. There could be numerous other situations where rational expressions are involved. Do some research. What do you find?
For this discussion activity, discuss an application of rational expression. Be sure to include the following components in your discussion. 1. A rational expression/equation 2. Restricted values of your variable (x, y, etc.), if any.
What is Rational Expression?Rational expression or equation is basically the method of calculation of real-life based problems related to:1. “Motion” related problems and 2. “Rate of Work” done by different people, related problems.Application of Rational Expression? For Motion Rational Expression, we use the “ Distance” or “Speed” formula Distance = Rate of Speed * Time is takend = r *tFor Example, The river has a current of 4 mph (Miles per hour). A Speed boat takes the same amount of time to go 30 miles downstream as it does to go 20 miles upstream, then what will be the speed of the boat in still water?Here, Distance for Downstream = 30 MilesDistance for Upstream = 20 MilesNow, let, X = Speed of a boat in still waterSo we have, X+4 = Speed of Downstream (as the current of the river is pushing the boat in Downstream)X-4 = Speed of Upstream (as the boat is sailing against the current of the river) Distance (d) Rate (r) Time (t)Downstream 30 X+4 30/(X+4)Upstream 20 X-4 20/(X-4)So, we have30/(X+4) = 20/(X-4)LDC: 20(X+4) = 30(X-4)20X + 80 = 30X – 120 200= 10XX = 200/10 = 20Therefore, the speed of boat in Still water is = X = 20Upstream water = X-4 = 20-4 = 16Downstream water = x+4 = 20+4 = 24So the speed of Boat is more in Downstream and Less in Upstream? Again for “Rate of Work “ Rational ExpressionLet me understand by taking an example Tom can paint the house is 7 hours, Jerry can do the same in 5 hours, How long will it take for them for working together to paint the same house?So let, X (hrs.) = the time take by both for working together7 hrs. = time taken by Tom5 hrs. = time taken by JerryWhole work is (suppose) = 1So, Rational Expression = (X/7) + (X/5) = 1Taking LCD: 35,(35X/7) + (35X/5) = 355x + 7X =3512X =35X= 35/12 hours.Cite of Source: Original work (It is not copied from any other Sources)