<PRE><B>Question 1205745</B>
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







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