Two trains depart at the same time from the same station and travel in opposite directions. One train travels 25 mph faster than the other train. After 2 hours the trains are 162 miles apart. Find the speed of each train.
Using algebra:
let x=speed of slower train
then x+25 = speed of faster train
After two hours, total distance travelled:
2(x + x+25) = 162 miles
divide by two to get
2x+25 = 81
2x=81-25=56
x=28 mph (slower train, it'd better be half price!)
faster train = 28+25 = 53 mph
Check: (28+53)*2=162 :)
By mental calculations, no pen, paper nor calculator:
Reasoning:
Over two hours, the faster train travelled 50 miles more than the slower. So if both travelled at the slower speed, they would have travelled a total of 162-50=112miles in two hours. Each (of the slower) will have a speed of 112/4=28 mph. The faster one, of course, travels at 28+25=53 mph.
To find the speed of each train, we can set up a system of equations based on the given information.
Let's denote the speed of the slower train as "x" mph.
Since the faster train is traveling 25 mph faster than the slower train, its speed can be represented as "x + 25" mph.
We know that the distance traveled by both trains is equal to the sum of their speeds multiplied by time. In this case, the time is 2 hours.
For the slower train:
Distance = Speed * Time
Distance = x * 2
Distance = 2x
For the faster train:
Distance = Speed * Time
Distance = (x + 25) * 2
Distance = 2x + 50
According to the problem, after 2 hours, the total distance between the trains is 162 miles. Therefore, we can set up the following equation:
2x + 2x + 50 = 162
Simplifying the equation:
4x + 50 = 162
4x = 162 - 50
4x = 112
x = 112 / 4
x = 28
So, the speed of the slower train is 28 mph.
To find the speed of the faster train, we can substitute the value of x back into the equation:
Speed of faster train = Speed of slower train + 25
Speed of faster train = 28 + 25
Speed of faster train = 53 mph
Therefore, the speed of the slower train is 28 mph, and the speed of the faster train is 53 mph.