The speed of a passenger train is 8 mph faster than the speed of a freight train. The passenger train travels 310 miles in the same time it takes the freight train to travel 270 miles. Find the speed of each train.
What is the speed of passenger train?
What is the speed of freight train?
Please help thank you, i suck at story problems
p = f + 8
310 / p = 270 / f ... 310 f = 270 p
310 f = 270 (f + 8)
310 f = 270 f + (8 * 270)
40 f = 8 * 270
Sure, I can help you solve this problem.
Let's assume the speed of the freight train is "x" mph. According to the problem, the speed of the passenger train is 8 mph faster, so the speed of the passenger train would be "x + 8" mph.
Now, let's use the equation: distance = speed × time.
For the passenger train, we know that it travels 310 miles at a speed of "x + 8" mph, and we want to find the time it takes. So, we can write the equation as:
310 = (x + 8) × time
For the freight train, we know that it travels 270 miles at a speed of "x" mph, and we want to find the time it takes. So, we can write the equation as:
270 = x × time
Now, we have two equations with two unknowns (speed and time). We can solve this system of equations using substitution or elimination.
Let's solve the second equation for time:
time = 270 / x
Substitute this expression for time in the first equation:
310 = (x + 8) × (270 / x)
Now, we can solve for x by cross multiplying:
310x = (x + 8) × 270
Distribute on the right side:
310x = 270x + 2160
Subtract 270x from both sides:
40x = 2160
Divide both sides by 40:
x = 2160 / 40
Simplifying further:
x = 54
So, the speed of the freight train is 54 mph.
To find the speed of the passenger train, substitute this value back into either of the original equations. Let's use the second equation:
time = 270 / x
time = 270 / 54
time = 5
Now substitute this value of time into the first equation:
310 = (x + 8) × time
310 = (54 + 8) × 5
310 = 62 × 5
310 = 310
Therefore, the speed of the passenger train is 54 + 8 = 62 mph.
To summarize:
- The speed of the passenger train is 62 mph.
- The speed of the freight train is 54 mph.