SOLUTION: A bus traveled 2 hours at a certain speed, then decreased the speed by 20 miles/hr and traveled for 3 more hours. If the total distance traveled is estimated between 250 miles and

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Question 156928: A bus traveled 2 hours at a certain speed, then decreased the speed by 20 miles/hr and traveled for 3 more hours. If the total distance traveled is estimated between 250 miles and 330 miles, find the range of the initial speed of the bus.
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
bus traveled 2 hours at x miles per hour.
bus traveled 3 hours at (x-20) miles per hour.
total distance was between 250 and 330 miles.
solve each separately.
rate * time = distance, so ...
250 = 2*x + 3*(x-20) = 2*x + 3*x - 60.
310 = 5*x (add 60 to both sides of the equation to eliminate the 60 from the right hand side).
x = 62 miles per hour.
bus traveled 2 hours at 62 miles per hour and 3 hours at 42 miles per hour.
calculating out at these rates yields 124 + 126 = 250 so the answer checks out.
that's the low end.
the high end is as follows:
330 = 2.x + 3.(x-20) = 2*x + 3*x - 60.
390 = 5*x (add 60 to both sides of the equation to eliminate the 60 from the right hand side).
x = 78 miles per hour.
bus traveled 2 hours at 78 miles per hour and 3 hours at 58 miles per hour.
calculating out yields 156 + 174 = 330 so the answer checks out.
final answer is:
bus travels between 62 miles per hour and 78 miles per hour for 2 hours and then travels between 42 miles per hour and 58 miles per hour for 3 hours.