SOLUTION: You and your family are going to lousiville from Memphis at the rate of 40 mi/h. Your uncle is going to Memphis from louisville at a rate of 60 mi/h. He leaves two hours later. The

Question 345982: You and your family are going to lousiville from Memphis at the rate of 40 mi/h. Your uncle is going to Memphis from louisville at a rate of 60 mi/h. He leaves two hours later. The two cities are 380 miles apart, at what time do the cars meet?
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
Let T be the number of hours past noon the two cars meet.
We know that the first car travels 40*T (D=R*T) miles when the two cars meet.
The second car will have traveled 60*(T-2) hours when the two cars meet.
The total distance traveled by both cars will be 380 miles so:
40*T + 60*(T-2) = 380
40*t+60*(t-2)=380
Multiply 40 by t to get 40t.
40t+60*(t-2)=380
Multiply all the factors separated by a * in 40*t+60*(t-2).
40t+60(t-2)=380
Multiply 60 by each term inside the parentheses.
40t+60t-120=380
Since 40t and 60t are like terms, add 60t to 40t to get 100t.
100t-120=380
Since -120 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 120 to both sides.
100t=120+380
Add 380 to 120 to get 500.
100t=500
Divide each term in the equation by 100.
(100t)/(100)=(500)/(100)
Simplify the left-hand side of the equation by canceling the common factors.
t=(500)/(100)
Simplify the right-hand side of the equation by simplifying each term.
t=5:00 pm
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