Question 761147
This is what I came up with.
Distance = Rate x time.
T = time in hours
We will call the distance between the two trains X. (This will later be removed from the equation)
The rate of each train will be written as X(The total distance) divided by the time it takes for the train to cover the total distance.
Our equation wil be: {{{T*(X/4) + T*(X/7) = X}}}
Since every term contains an X we can divide both sides by X to remove it.
{{{T*(1/4) + T*(1/7) = 1}}}
I am going to rewrite the equation.
{{{(T/4) + (T/7) = 1}}}
Since the denominators are different multiply everything by 7 and by 4 to get them in the same units.
{{{(T/cross(4))*7 *cross(4) + (T/cross(7))*cross(7)*4 = 1*7*4}}}
{{{7T + 4T = 28}}}
Combine like terms
{{{11T = 28}}}
Divide both sides by 11
{{{highlight(T = 2.545)}}}
Now you have convert the 0.545 hours to minutes.
{{{(0.545cross(hours)/1)*(60minutes / 1cross(hours)) = 32.7}}}
Add the 2 hours and 32.7 minutes to the time of 8:00AM.
The trains should pass around 10:33AM