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

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) (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.
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