Question 1059932
distance = rate x time
d = rt


One Train:
rate = 90
time = t
d = 90t   {distance = rate x time}


Other Train
rate = 120
time = t - 2   {left 2 hours later}
d = 120(t - 2)   {distance = rate x time}


When the faster train catches up with the slower train, their distances will be equal.


90t = 120(t - 2)   {set distances equal to each other}
90t = 120t - 240   {used distributive property}
-30t = -240   {subtracted 120t from each side}
t = 8   {divided each side by -30}


t - 2 corresponds to the time of the faster train
=  8 - 2   {substituted 8, in for t, into (t - 2)
= 6   {subtracted}


It will take the faster train 6 hours to catch up with the slower train.
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