SOLUTION: emily and Camille started from the same city and drove in opposite directions on the freeway. After 3 hours they were 354 miles apart. If they had gone in the same direction, Emily

Question 566561: emily and Camille started from the same city and drove in opposite directions on the freeway. After 3 hours they were 354 miles apart. If they had gone in the same direction, Emily would have been 18 miles ahead of Camille. How fast did each woman drive?
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Since they were traveling in opposite directions, they were moving apart at the sum of their speeds. Since they were 354 miles apart in 3 hours, the sum of their speeds must be 116 mph. Had they been going in the same direction, their distance apart would have been a function of the difference in their speeds. 18 miles in 3 hours is 6 mph difference.

Solve the 2X2 system.

John

My calculator said it, I believe it, that settles it

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
emily and Camille started from the same city and drove in opposite directions on the freeway. After 3 hours they were 354 miles apart.
Let e be Emily's rate; let c be Camille's rate
----
distance + distance = 354 miles
3e + 3c = 354
e + c = 118
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If they had gone in the same direction, Emily would have been 18 miles ahead of Camille. How fast did each woman drive?
3e - 3c = 18
e - c = 6
=======================
Two equations:
e + c = 118
e - c = 6
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Add and solve for "e":
2e = 124
e = 62 mph (Emily's rate)
------
Solve for "c":
e + c = 118
62 + c = 118
c = 56 mph (Camille"s rate)
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Cheers,
Stan H.
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