SOLUTION: I have a assignment on making two linear equations from two animals racing a fair race. The two I picked were African wild dog 45mph and coyote 43mph. How would I make that into an

Question 1085553: I have a assignment on making two linear equations from two animals racing a fair race. The two I picked were African wild dog 45mph and coyote 43mph. How would I make that into an equation. I am so lost and confused
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
assume the race is for 1 mile.

rate * time = distance.

for the dog, rate = 45 miles per hour.

for the coyote, rate = 43 miles per hour.

let T1 equal the time it takes the dog to run a distance of D1.

let T2 equal the time it takes the coyote to run a distance of D2.

the formulas become:

45 * T1 = D1

43 * T2 = D2

if you make the distance that they both run the same, then replace D1 and D2 with D.

you will get:

45 * T1 = D

43 * T2 = D

if you subtract the second equation from the first, you will get:

45 * T1 - 43 * T2 = 0

add 43 * T2 to both sides of the equation to get 45 * T1 = 43 * T2

divide both sides of the equation by 45 to get T1 = 43 * T2 / 45

simplify to get T1 = .9556 * T2 rounded to 4 decimal digits.

the dog is faster and will run the same distance in less time than the coyote.

if you make the time the same, then replace T1 and T2 with T and the formulas become:

45 * T = D1

43 * T = D2

solve both formulas for T to get:

T = D1 / 45

T = D2 / 43

subtract the second equation from the first and you get:

0 = D1/45 - D2/43

add D2/43 to both sides of the equation to get D2/43 = D1/45

solve for D1 to get D1 = D2/43 * 45.

simplify to get D1 = 1.0465 * D2 rounded to 4 decimal places.

given they run the same time, the dog will run 1.0465 times the distance that the coyote will run.

stand to reason, because the dog is faster than the coyote.

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