A train leaves Manila at 3:00 AM, averaging 50mph. Another train headed in the opposite direction leaves Manila at 4:00 AM, averaging 60mph. How far (in miles) are the two trains from each other at 6:00 AM?

The answer is 270.

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We can use the formula,

$\large\boxed{d=Vt}$ where: $d$ =distance, $V$ = speed and $t$ =time

Considering the train that leaves at 3:00 pm:The total time it travels from $3:00~pm$ to $6:00~pm$ is $3$ hours. So we have

$d_1=V_1t_1=50(3)=150~miles$

Considering the train that leaves at 4:00 pm:The total time it travels from $4:00~pm$ to $6:00~pm$ is $2$ hours. So we have

$d_2=V_2t_2=60(2)=120~miles$

Finally, the distance between them at exactly $6:00~pm$ is

$d=d_1+d_2=150+120=$ $\large\boxed{\color{#D61F06}270~miles}$ $\color{#3D99F6}\boxed{\large\text{answer}}$