A train leaves Manila at 11:00 PM, averaging 80mph. Another train headed in the same direction leaves Manila at 1:00 AM, averaging 100mph. How many hours after the second train leaves will it overtake the first train?

The answer is 8.

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We can use the formula $\boxed{d=Vt}$ where: $d$ =distance, $V$ =speed and $t$ =time

Considering the first train:The distance traveled is

$d_1=V_1t_1=80(t+2)=80t+160$ $\implies$ note that $2$ was added because it started $2$ hours earlier than the second train

Considering the second train:The distance traveled is

$d_2=V_2t_2=100t$

Now, we know that $d_1$ must be equal to $d_2$ , so

$d_1=d_2$

$80t+160=100t$

$20t=160$

$\large\boxed{\color{#20A900}t=8~hours}$ $\color{#EC7300}\boxed{\text{answer}}$