A train leaves a station and travels north at a speed if 50 mph. Five hours later, a second train leaves on a parallel track and travels north at 175 mph. How far from the station will they meet?
distance1=50t
distance2=175(t-5)
subtract first equation from second, solve for t:
d1-d2=0=125t-5*175
divide by 5, then
25t=175
t=7 hrs
distance=7*50
Pepet
To find out how far from the station the two trains will meet, we need to determine the total distance traveled by each train until they meet. Since the second train leaves 5 hours later than the first train, we can calculate the distance traveled by each train separately.
Let's start with the first train. Since it travels at a speed of 50 mph, and it departs 5 hours earlier than the second train, we need to calculate the distance it has traveled in 5 hours.
Distance = Speed × Time
Distance = 50 mph × 5 hours
Distance = 250 miles
Therefore, the first train has traveled 250 miles when the second train starts.
Now let's calculate the distance traveled by the second train. Since it travels at a speed of 175 mph and the first train has already traveled for 5 hours, we need to find the total time it takes for the second train to meet the first train. Let's call this time "t."
The time for the second train to meet is the same as the total time for both trains to meet. So we can set up an equation:
50 mph × (t + 5 hours) = 175 mph × t
Now let's solve this equation to find the value of "t":
50t + 250 = 175t (distribute the 50 mph)
250 = 175t - 50t (move the 50t to the left side)
250 = 125t (combine like terms)
t = 250 / 125 = 2 hours
We have found that it will take 2 hours for the second train to meet the first train.
Now, to determine the distance from the station where they will meet, we need to calculate the distance traveled by the second train during these 2 hours.
Distance = Speed × Time
Distance = 175 mph × 2 hours
Distance = 350 miles
Therefore, the two trains will meet 350 miles from the station (which is the distance traveled by the second train when they meet).