Question

Jake drives a tractor from one town to another, a distance of 180 kilometers. He drives 9 kilometers per hour faster on the return trip, cutting 1 hour off the time. How fast does he drive each way?

Answer 1

given the following information

Distance= 180km

Speed first trip (S1)= S km/h

Speed on the return trip (S2)= S+9 km/h

the time first trip (t1) = t h

the time in the retunr trip ( t2)= t -1 h

since speed=D/t

we have the following equations

Eq1

`S1=(180)/(t)`

and

Eq2

`S1+9=(180)/(t-1)`

notice we have 2 equations and 2 variables

then Using eq1 in eq 2

`(180)/(t)+9=(180)/(t-1)`

solving for t

`180\left(t-1\right)+9t\left(t-1\right)=180t`
`180t-180+9t^2-9t=180t`
`-180+9t^2-9t=0`

applying quadratic Formula

t=5 and t=-4

then

`S1=(180)/(5);S1=(180)/(-4)`
`S1=36;S1=-45`

notice the speed A=36, B=-45

a negative symbol in speed represents direction

wich makes sense due to Jake is driving back home

then

the speed going is

S1=36

the speed returning is

S2=36+9=45