004 Sample Final A, Problem 12

Set up, but do not solve the following word problem. Two private airplanes travel toward each other from cities that are 780 km apart at speeds of 190 km/hr and 200 km/hr. They left at the same time. In how many hours will they meet?

Foundations
What is the formula for distance?
Answer:
The formula for distance is d=rt where r is the rate and t is the time.

Solution:

Step 1:
The distance formula for the plane traveling 190km/hr is $190t=d$.

Step 2:
The other plane starts off 780km away from the first plane. So, this plane's distance is 780-d where d is the distance of the first plane.
So, the distance formula for this second plane is $200t=780-d$.

Step 3:
Now, adding these two equations together, we get $390t=780$. So, $t=2$ hours.

Final Answer:
2 hours

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