Question 341418: One train runs 90% of the time and goes 55 mph any time it runs (no acceleration time lag). Another train runs 10% of the time. How fast does this train have to go (mph) to exceed the distance of the other train?
Hint: Examine the speeds of the train for many, many hours to come up with the speed as a whole number.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! One train runs 90% of the time and goes 55 miles per hour.
The other train runs 10% of the time.
The total distance that each train will travel is given by D.
The formula we will work with is R * T = D.
The first travels 90% of the Time, so the first train will achieve D in .9*T
The formula for the first train will be R * .9*T = D
Since R = 55 miles per hour, then the formula for the first train becomes 55 * .9*T = D which becomes 49.5 * T = D.
The formula for the second train is R * .1*T = D
We want to find an equation where the distance traveled by the second train exceeds (is greater than) the distance traveled by the first train.
This means that D for the second train is greater than D for the second train.
Since for the first train, we know that 49.5 * T = D, and for the second train we know that R * .1 * T = D, then we can assume that:
49.5 * T = R * .1 * T because they are both equal to the same thing and are therefore equal to each other.
Since we want the D of second train to be greater than the D of the first train, then we change our equation to read:
49.5 * T < R * .1 * T.
If we divide both sides of this equation by T, then we should get:
49.5 < .1 * R
If we further divide both sides of this equation by .1, then we should get:
495 < R
It appears that the second train must travel at a rate greater than 495 miles per hour in order to exceed the distance traveled by the first train.
Let's see if that holds true.
Assume the first train travels at 55 miles per hour.
Assume the second train travels at 495 miles per hour.
Assume the total time is 10 hours.
This means that the first train is traveling for 9 hours and the second train is traveling 1 hour.
9 * 55 = 495
1 * 495 = 495
They travel the same distance.
Now assume the second train travels at a speed greater than 495 miles per hour.
Assume the second train is traveling at 500 miles per hour.
9 * 55 is still 495.
1 * 500 is 500 which is greater than 495.
The answer looks good.
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