The freight train runs 12miles per hour than a passenger train. It runs 65miles in the same time that the passenger train runs 165miles find the rate of each train. I don't really know the formula using quadratic im sorry
I suspect typos and there is no quadratic involved as it is stated.
v = passenger train speed
(v - 12) = freight train speed
(v-12)t = 65
v t = 165
so
65/(v-12) = 165/v
65 v = 165 v - 1980
100 v = 1980
v = 19.8 mph
v-12 = 7.8
it quadratic word problem.
No problem! To solve this problem, we can set up a system of equations using the information given. Let's assume the rate of the passenger train is x miles per hour.
According to the problem, the freight train runs 12 miles per hour faster than the passenger train. Therefore, the rate of the freight train would be x + 12 miles per hour.
Now, we need to find the time it takes for each train to travel their respective distances. We can use the formula:
Time = Distance / Rate
For the passenger train, the distance is 165 miles and the rate is x miles per hour:
Time for passenger train = 165 / x
For the freight train, the distance is 65 miles and the rate is (x + 12) miles per hour:
Time for freight train = 65 / (x + 12)
According to the problem, the time taken by both trains is the same. So, we can set up an equation:
Time for passenger train = Time for freight train
165 / x = 65 / (x + 12)
Now, we can solve this equation to find the value of x, which represents the rate of the passenger train.
To do this, let's cross-multiply:
165 * (x + 12) = 65 * x
165x + 1980 = 65x
165x - 65x = -1980
100x = -1980
Dividing both sides by 100 gives us:
x = -1980 / 100
x = -19.8
Since the rate of a train cannot be negative, we need to discard this solution. It means there is no real solution for the rate of the passenger train.
Therefore, there is no rate for the passenger train that satisfies the given conditions.