Two trains, one going from Boston to New York and the other going from New York to Boston, started their trips at exactly same time. Speed of the first train was 10 miles per hour less than twice the speed of the second train. How far from Boston station have they met, if the total distance between the cities along the rail road is 220 miles?

140

just waking up in the morning gotta thank god, I dont know but today seems kinda odd

To find the distance from the Boston station where the two trains meet, we need to set up an equation based on the information given.

Let's say the speed of the second train is x miles per hour. According to the question, the speed of the first train is 10 miles per hour less than twice the speed of the second train, which means it is (2x - 10) miles per hour.

The key thing to remember is that when they meet, the total distance each train has traveled is equal to the total distance between the cities (220 miles).

Now, let's use the formula distance = speed × time to establish the equation for each train.

For the first train:
distance traveled = (2x - 10) * time

For the second train:
distance traveled = x * time

Since both trains started at the same time, they have traveled for the same amount of time, so the time can be the same for both equations.

By equating the distances, we get the following equation:
(2x - 10) * time = x * time

Now, we cancel out the time variable as it is the same for both sides of the equation:
2x - 10 = x

Next, we solve for x:
2x - x = 10
x = 10

So, the speed of the second train, which is going from New York to Boston, is 10 miles per hour.

Now we can find the time it takes for both trains to meet. Since distance = speed × time, we can rearrange the equation to find the time:
time = distance / speed
time = 220 miles / 10 miles per hour
time = 22 hours

Finally, we can find the distance from the Boston station where they meet by multiplying the speed of the second train by the time it took to meet:
distance = speed * time
distance = 10 miles per hour * 22 hours
distance = 220 miles

Therefore, the two trains have met at a distance of 220 miles from the Boston station.

speed of second train ---- x mph

speed of first train --- 2x-10 mph

When they meet they would have traveled the same time
let that time be t hrs

distance gone by first train = tx
distance gone by 2nd train = t(2x-1)

tx + t(2x-1) = 220
tx + 2tx - t = 220
t(3x-1)=220
t = 220/(3x-1)

I don't think we have enough information, since I can pick different values for x , and get valid answers
e.g. let x = 20 mph
then t = 220/(59) = 3.7288 hrs

then they meet after tx or 74.57 miles
the other distance is t(2x-1) = 145.42
they add up to 119.99 miles

e.g. let x = 40 mph
then t = 220/119 = 1.8487.. hrs
distance = 73.95 miles
etc