# Rational Equations- Applications with Uniform Motion (Part 1)

In this example we’re going to discuss a

uniform motion problem involving a rational equation and we’ll use factoring to solve Caitlyn went on a 56-mile trip to a soccer game

on the way back due to road construction she

had a drive 28 miles per hour slower this made the trip take 1 hour longer how fast

did she drive to the soccer game we can recall that with uniform motion problems we use a specific formula

0:00:35.033,0:00:35.000

we can rewrite this equation rate times time equals distance however with

rational equations we can rewrite this equation as either T equals distance over R and this is if

we want to find the rate or rewrite it is as r equals d over T and this is

where we would want a find the time in this case we are looking for how fast did she drive so fast means the rate so we use this formula d over r so let’s go ahead and make a table R, T and D we have two categories going to the soccer

game and coming from the soccer game the rate in which she drove to the soccer game

is unknown but we do know something about the return trip that she drove 28 miles per hour

slower so slower means we’re are going to subtract we also know that it made the trip take 1 hour

longer meaning whatever time it took her to get

to the soccer game it took her even longer meaning adding 1 hour

to get home the distance to the soccer team is 56 and from

will also be 56 so setting up our equation using the equation T equals D over R we get T going to the soccer game equal to the

distance 56 over the rate in this case R T being a time from the soccer game that was

given as T plus one equals the rate 56 over the rate R-28 our goal is to set the times equal to each other we want to set T from the soccer game equal to the time going to the soccer game we really

can’t do that right now because we have 1 on the left side so subtract one from each side

and isolate the time going from the game so here we get T from the game and the ones cancel we’re left with 56 over

R-28 minus 1 great these are the equations and we’ll set them equal to each other so the time it took to get from the soccer game is 56 divided by R-28 minus 1 equal to the time it took to get to the soccer game which

is 56 divided by R and now we have to do is solve and we can find the rate