Question

At midnight, a passenger train left the station. Two hours later, a freight train left the same station

traveling on the same track in the same direction. At 8 a.m. the passenger train was 120 miles ahead
of the freight train. Find the rate of each train if the passenger train traveled 5 mph faster than the
freight train. ENTER ONLY THE NUMBER (do not enter variables, punctuation marks, units, symbols
or equals signs).

Answer 1

speed of freight train = 40 MPH

speed of passenger train = 45MPH

Explanation:

Let the speed of freight train be X miles per hour

speed of passenger train is 5 mph more than speed of freight train

Therefore speed of passenger train is X + 5 mph

we will use the formula to calculate distance which is givn below

distance travelled by any object is = speed * time

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Time at which the distance between the train are calculated = 8 AM

for freight train

since it started at 2 AM morning and traveled until 8 AM

duration for which it traveled = 8 - 2 = 6 hours

distance traveled by freight train in those 6 hours = speed of freight train * duration for which it travelled = X * 6 = 6X ----equation A

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for passenger train

since it started at 00.00AM morning and traveled until 8 AM

duration for which it traveled = 8 - 0 = 8 hours

distance traveled by passenger train in those 8 hours = speed of passenger train * duration for which it travelled = X + 5 * 8

= 8X + 40 ------- equation B

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Distance between passenger train and freight train at 8 AM = 120 miles

also distance can be calculated using distance calculated above in equation A and B

Distance between passenger train and freight train at 8 AM in terms if X = distance traveled by passenger train in 8 hours - distance travelled by freight train in 6 hours = 8X + 40 - 6X = 2X + 40

2X + 40 distance is equal to 120 miles as given in question

therefore

2X + 40 = 120

2X = 120 -40

X = 80/2 = 40

therefore speed of freight train = X = 40 MPH

speed of passenger train = X + 5 = 40 + 5 = 45MPH