Answer :
-- The passenger train is traveling 16 mph faster than the freighter,
so it gains 16 miles on the freighter every hour.
-- If the passenger train overtakes the freighter after 7.125 hours,
then it gained (7.125 x 16) = 114 miles on it in order to overtake it.
-- But that was just the lead that the freighter built up in the first 3 hours.
So the freighter's speed is 114/3 = 38 miles per hour.
And the passenger train's speed is 54 mph.
Check:
-- The passenger train traveled at 54 mph for 7.125 hours = 384.75 miles
-- The freighter traveled at 38 mph for 10.125 hours = 384.75 miles
-- The distances are equal, so that's when one overtook the other, and
they were both in the same place.
so it gains 16 miles on the freighter every hour.
-- If the passenger train overtakes the freighter after 7.125 hours,
then it gained (7.125 x 16) = 114 miles on it in order to overtake it.
-- But that was just the lead that the freighter built up in the first 3 hours.
So the freighter's speed is 114/3 = 38 miles per hour.
And the passenger train's speed is 54 mph.
Check:
-- The passenger train traveled at 54 mph for 7.125 hours = 384.75 miles
-- The freighter traveled at 38 mph for 10.125 hours = 384.75 miles
-- The distances are equal, so that's when one overtook the other, and
they were both in the same place.
From the question:
Passenger Train (PT)
Freight Train (FT)
As at when it is 7.125 hours, when the PT meets up the FT,
If the FT has been traveling for x miles per hour, then
The PT which is faster is traveling (x+16) miles per hour.
Since the PT has traveled 7.125 hours, the FT would have traveled for (7.125 + 3) = 10.125.
As at when both trains meet, the distances traveled by both are equal.
Distance = Speed * time
PT = FT
(x+16)*7.125 = x(10.125)
7.125x + 16*7.125 = 10.125x
7.125x + 114 = 10.125x
114 = 10.125x - 7.125x
114 = 3x
x = 114/3
x = 38
Therefore FT had been traveling speed of 38 miles per hour.
Of course you know the PT is 16 miles per hour faster = 38 + 16 = 54 miles per hour.
I hope this helps.
Passenger Train (PT)
Freight Train (FT)
As at when it is 7.125 hours, when the PT meets up the FT,
If the FT has been traveling for x miles per hour, then
The PT which is faster is traveling (x+16) miles per hour.
Since the PT has traveled 7.125 hours, the FT would have traveled for (7.125 + 3) = 10.125.
As at when both trains meet, the distances traveled by both are equal.
Distance = Speed * time
PT = FT
(x+16)*7.125 = x(10.125)
7.125x + 16*7.125 = 10.125x
7.125x + 114 = 10.125x
114 = 10.125x - 7.125x
114 = 3x
x = 114/3
x = 38
Therefore FT had been traveling speed of 38 miles per hour.
Of course you know the PT is 16 miles per hour faster = 38 + 16 = 54 miles per hour.
I hope this helps.