A passenger train travels 392 miles in the same time that it takes freight train to travel 322 miles. If the passenger train travel 20 miles per hour faster than the freight train.Find the rate of each train.
392mi/t = 322/t + 20.
392 = 322 + 20t.
20t = 392 - 322 = 70.
t = 3.5 h.
r = 392mi/3.5h = 112 mi/h = Speed of the
P. train.
r = 322mi/3.5h = 92 mi/h = Speed of the
F. train.
Let's assume the rate of the freight train is "x" mph.
Since the passenger train travels 20 mph faster than the freight train, its rate is "x + 20" mph.
We can use the formula: Time = Distance / Rate.
For the passenger train:
Time = 392 / (x + 20)
For the freight train:
Time = 322 / x
Since both trains take the same time to travel their respective distances, we can set the two equations equal to each other:
392 / (x + 20) = 322 / x
To solve for x, we can cross-multiply:
392x = 322(x + 20)
392x = 322x + 6440
70x = 6440
x = 92
The rate of the freight train is 92 mph.
Therefore, the rate of the passenger train is 92 + 20 = 112 mph.
To solve this problem, we need to find the rates at which both trains are traveling. Let's assume the rate of the passenger train is "x" miles per hour.
Given that the passenger train travels 392 miles in the same time it takes for the freight train to travel 322 miles, we can set up the following equation:
Time taken by the passenger train = Time taken by the freight train
392 / x = 322 / (x - 20)
We use the equation because time = distance / speed.
Cross-multiplying the equation, we get:
392(x - 20) = 322x
Now, let's solve the equation to find the value of x:
392x - 392(20) = 322x
392x - 7840 = 322x
392x - 322x = 7840
70x = 7840
x = 7840 / 70
x = 112
Therefore, the rate of the passenger train is 112 miles per hour.
To find the rate of the freight train, we subtract 20 from the rate of the passenger train:
Rate of the passenger train = x = 112 miles per hour
Rate of the freight train = x - 20 = 112 - 20 = 92 miles per hour
Hence, the rate of the passenger train is 112 miles per hour, and the rate of the freight train is 92 miles per hour.