A train travels a distance of 90 miles from A to B in one hour. Another train sets off at the same time and travels from B to A, taking two hours to complete the journey. How many miles from A did the two trains cross?
When they meet, they will have traveled for the same time.
Let that time be t hrs.
let the distance covered by the fast train be x miles, then distance covered by the slower train is 90-x
time for faster train = x/90
time for slower train = (90-x)/45
x/90 = (90-x)/45
45x = 8100- 90x
135x = 8100
x = 60
check:
time taken to go 60 miles for fast train = 60/90 = 2/3 hr
time taken for slower train to go 30 miles = 30/45= 2/3
To find the point where the two trains crossed, we need to determine the distance traveled by each train before they met.
Let's assume the point where the two trains crossed is C, which is x miles from point A.
Train 1 travels a distance of 90 miles in one hour from point A to point B. Since the second train takes two hours to travel from point B to point A, its speed must be half of Train 1's speed.
Since time = distance / speed, the speed of Train 2 is 90 miles / 2 hours = 45 mph.
Now let's calculate the distance each train traveled before they met:
Distance traveled by Train 1 = 90 - x miles (from point B to point C)
Distance traveled by Train 2 = 45 * 2 = 90 miles (from point A to point C)
Since the total distance covered is the same for both trains when they meet, we can equate the distances traveled by each train:
90 - x = 90
Simplifying the equation:
-x = -90
x = 90
Therefore, the two trains crossed each other 90 miles from point A.
To find the point where the two trains cross, we need to determine the distance traveled by each train during the given time frame.
Let's call the point where the trains cross "C." Train A starts at point A and moves towards point B, while Train B starts at point B and moves towards point A. Both trains travel at a constant speed.
Train A travels a distance of 90 miles in one hour, so its speed is 90 miles per hour (mph).
Train B takes two hours to complete the journey from point B to point A. Since the distance is the same as Train A, we can calculate its speed using the equation: speed = distance / time. In this case, the speed of Train B is 90 miles / 2 hours = 45 mph.
Now that we have the speeds of both trains, we can calculate the distances they have traveled to reach point C.
Let's assume that Train A traveled x miles from point A to point C, and Train B traveled y miles from point B to point C.
Since both trains started at the same time, they have traveled for the same amount of time when they meet at point C. We can use the equation: time = distance / speed.
For Train A: time = x miles / 90 mph.
For Train B: time = y miles / 45 mph.
Since both trains traveled for the same time, we can set up an equation: x miles / 90 mph = y miles / 45 mph.
To solve this equation, we can multiply both sides by 90: x miles = (y miles / 45 mph) * 90 mph.
Simplifying: x miles = 2y miles.
Now we need to find the values of x and y that satisfy this equation. We know that Train A traveled a total distance of 90 miles, so x + y = 90.
Substituting the value of x from the previous equation: 2y + y = 90.
Combining like terms: 3y = 90.
Dividing both sides by 3: y = 30.
Now we know that Train B traveled 30 miles from point B to point C. Substituting this value back into the equation x + y = 90: x + 30 = 90.
Solving for x: x = 90 - 30 = 60.
Therefore, the two trains crossed 60 miles from point A.