Hilary rode her horse for 8 miles until it was hurtThen she

Hilary rode her horse for 8 miles until it was hurt.Then she walked back home to call a vet. She figures the horse wals twice as fast as she does. the whole trip took 4 hours, so how fast would Hilary have to walk?

Solution

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.