An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions. The eastbound train travels 12 miles per hour faster than the westbound train. After 1.5 hours, they are 174 miles apart. At what speeds are the two trains traveling?
where you get 64 from.
speed of westbound train -- x mph
speed of eastbound train -- x+12
1.5x + 1.5(x+12) = 174
1.5x + 1.5x + 18 = 174
3x = 156
x = 52
westbound train --- 52 mph
eastbound train ---- 64 mph
check"
1.5(52) = 78
1.5(64) = 96
78+96 = 174
answer is correct.
They added 52+12=64 and the eastbound train speed since that train was traveling 12 miles faster than the westbound.
Well, let's call the speed of the westbound train "x" mph. That means the eastbound train is going at x + 12 mph. After 1.5 hours, the westbound train has traveled a distance of 1.5x miles, and the eastbound train has traveled a distance of 1.5(x + 12) miles.
Since they are on parallel tracks, their distances add up to 174 miles. So we have the equation 1.5x + 1.5(x + 12) = 174.
Now, let me do some quick math calculations... *scratches head* Okay, I'm done! So, after calculating, we find that the westbound train is going 54 mph, and the eastbound train is going 66 mph. Voila!
To find the speeds of the two trains, let's suppose the westbound train is traveling at x mph.
We are given that the eastbound train is traveling 12 mph faster, so its speed would be (x + 12) mph.
In 1.5 hours, the westbound train has traveled a distance of 1.5x miles, and the eastbound train has traveled a distance of 1.5(x + 12) miles.
According to the problem, the total distance between the two trains after 1.5 hours is 174 miles. So, we can write the following equation:
1.5x + 1.5(x + 12) = 174
Now, let's solve this equation to find the value of x:
1.5x + 1.5x + 18 = 174
3x + 18 = 174
3x = 174 - 18
3x = 156
x = 156 / 3
x = 52
Therefore, the westbound train is traveling at 52 mph, and the eastbound train is traveling at (52 + 12) mph, which is 64 mph.