Question 102480: It takes 1 hour longer to fly to St. Paul at 200 mi/h than it does to return at 250 mi/h. How far away is St. Paul?
Answer by mjgulinello(10)   (Show Source):
You can put this solution on YOUR website! Let t = the time in hours that it takes to fly to St. Paul at 250mph.
Since it takes 1 hour longer to fly there at 200mph, this will = t+1.
We know the distance to and from St. Paul is the same, so we can represent this distance two ways:
Distance = speed * time
D = 250t
and
D = 200(t+1)
Since the two distances are equal, we can now plug the first formula into the second one and get an equation with one variable.
250t = 200(t+1)
First use the distributive property on the right side of the equation.
250t = 200t + 200
Subtract 200t from each side of the equation.
50t = 200
Divide each side of the equation by 50.
t = 4
Now we know the time it takes to travel to St. Paul at 250mph is 4 hours.
Next, we plug that into the equation for distance.
D = 250t
D = 250 * 4
D = 1000
St. Paul is 1000 miles away.
We can check to make sure we got the right answer by using our second equation for distance.
D = 200(t+1)
D = 200 * (4+1)
D = 200 * 5
D = 1000
Our answer checks out. That's all for this problem.
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