Question 161162
The equation used in this problem is SpeedXTime=Distance

We know that the entire trip takes 4 hours 

Let us designate x as the time that it takes the horse to travel 8 miles

4-x= is designated as the time it takes Hilary to walk back

we also know the ratio of rate 2:1

Let us set up the equation

(Distance/Time)=speed of the horse  =8/x 
(Distance/Time)=speed of Hilary =8/4-x

We need to make both sides of the eqation equal. In order to do this we need to multiply (8/4-x) by 1/2 since the horse is going 2x the speed of Hilary


8/x=(1/2)(8/4-x)

Simplify by dividing 8 by 2 so that you get 8/x=4/4-x

Cross multiply to get 8(4-x)=4x

Use the distributive property

32-8x=4x

Add 8x to both sides and get

32=12x

Divide both sides by 12

x=1.33 hours it took the horse

4-x=2.67 hours it took Hilary


2.99 or 3 miles per hour

To double check let's plug in values


Speed(Time)=8
(3)2.67)=8.0 miles for Hillary

The horse speed is 8/1.33=6.0 mph


the horse is going 6/3 as fast as Hilary the answer is 2.