Question 986178
Distance = rate x time
d = rt


First train
d = rt
r = 55
t = time
d = 55t {the equation for the first train}


Second train
d = rt
r = 70
t - 0.5 = time {left 1/2 hour later}
d = 70(t - 0.5) {equation for second train}


When the second train overtakes the first train, their distances will be equal.


55t = 70(t - 0.5) {set distances equal to each other}
55t = 70t - 35 {used distributive property}
-15t = -35 {subtracted 70t from each side}
t = 2.3333 {divided each side by -15}


t = 2  1/3 hours


1/3 of an hour is 20 minutes


t = 2 hours and 20 minutes


Add 2 hours and 20 minutes onto first train's departure time:
7:00 + 2:20
= 9:20 


The second train will overtake the first train at 9:20 A.M.


How far will the first train be from the station:
55 mph for 2 hrs. and 20 minutes
= 55 x 2 1/3 {multiplied 55 by 2  1/3 hours}
= 55 x 7/3 {changed 2  1/3 to an improper fraction}
= 385/3 {multiplied through numerators}
= 128  1/3 miles from station
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