Question 1205745: Trashia left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 40 miles per hour. Half an hour later, Karissa left Riverside in her car on the same route as Trashia, driving 60 miles per hour. Solve the system:
{(40 y=60 x),(y=x+1/2) :}
A. for x to find out how long it will take Karissa to
catch up to Trashia.
B. What is the value of y the number of hours
Trashia will have driven before Karissa catches up
to her?
Found 3 solutions by greenestamps, Theo, josgarithmetic:
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
40y = 60x
y = x+1/2
When one of the two equations tells you precisely what one variable is in terms of the other, the obvious choice for a solution method is substitution. Replace "y" in the first equation with the equivalent expression "x+1/2".
40(x+1/2) = 60x
40x+20 = 60x
20 = 20x
x = 1
A. x is the number of hours Karissa drives. ANSWER: x = 1
B. y is the number of hours Trashia drives. ANSWER: y = x+1/2 = 1 1/2
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! your two equations that you show that need to be solved simultaneously are:
40y = 60x
y = x + 1/2
in the first equation, replace y with x + 1/2 from the second equation to get:
40 * (x + 1/2) = 60 * x
simplify to get:
40 * x + 40 * 1/2 = 60 * x
simplify further to get:
40 * x + 20 = 60 * x
subtract 40 * x from both sides of the equation to get:
20 = 60 * x - 40 * x
combine like terms to get:
20 = 20 * x
solve for x to get:
x = 1
go back to your original two equations and replace x with 1.
you get:
40y = 60x becomes 40y = 60 * 1
simplify to get 40y = 60
divide both sides of the equation by 40 to get:
y = 60/40 = 1.5
y = x + 1/2
replace x with 1 to get:
y = 1 + 1/2
combine like terms to get:
y = 1.5.
both equations get y = 1.5
your solution is x = 1 and y = 1.5
answers to your questions are:
A. for x to find out how long it will take Karissa to
catch up to Trashia.
trashia was traveling at 40 miles per hour.
karissa was traveling at 60 miles per hour.
y is the time that trashia was driving.
x is the time that karissa was driving.
since y = 1.5, then trashia was traveling for 1.5 hours at 40 miles per hour for a distance of 60 miles.
since x = 1, then karissa was traveling for 1 hour at 60 miles per hour for a distance of 60 miles.
karissa caught up to trashia at the 60 mile mark.
it took karissa 1 hour to catch up to trashia.
B. What is the value of y the number of hours
Trashia will have driven before Karissa catches up
to her?
y is equal to 1.5 hours.
x is equal to 1 hour.
trashia was driving for 1.5 hours before karissa caught up to her.
i usually solve problems like these as follows:
the basic formula is rate * time = distance.
for trashia, the formula becomes 40 * y = d
40 is the rate, y is the time, d is the distance.
for karissa, the formula becomes 60 * x = d
60 is the rate, x is the tie, d is the distance.
you are then given tht y = x + 1/2.\
the two formulas become:
40 * (x + 1/2) = d
60 * x = d
since they are both equal to d, you can set the expressions on the left side of each equation equal to each other to get:
40 * (x + 1/2) = 60 * x
simplify to get:
40 * x + 20 = 60 * x
subtract 40 * x from both sides of the equation to get:
20 = 20 * x
solve for x to get:
x = 1
since y = x + 1/2, you get y = 1.5
i only mentioned all this to let you know that you were dealing with a basic rate * time = distance type formula.
if you find that informative, fine.
if not, distregard.
any additional questions or concerns regarding this problem can be addressed to me.
theo
Answer by josgarithmetic(39617)  (Show Source):
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