Hilary rode her horse for 8 miles until it was hurt.Then she walked .pdf

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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..

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.

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1. 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

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