SOLUTION: a passenger train leaves the station 3 hours after a freight train left the same station. the freight train travels 30 mph slower than the passenger train. Find the rate of each if

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Question 526667: a passenger train leaves the station 3 hours after a freight train left the same station. the freight train travels 30 mph slower than the passenger train. Find the rate of each if the passenger train catches up with the freight traing in 4 hours
Found 3 solutions by ankor@dixie-net.com, lwsshak3, oberobic:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
a passenger train leaves the station 3 hours after a freight train left the same station.
the freight train travels 30 mph slower than the passenger train.
Find the rate of each if the passenger train catches up with the freight train in 4 hours
:
Let s = speed of the freight
then
(s+30) = speed of the pass train
:
From the given information we know the freight traveled 7 hrs, the pass 4 hrs
:
When the pass catches the freight, they will have traveled the same distance.
Write dist equation, dist = speed * time
:
Pass dist = freight dist
4(s+30) = 7s
4s + 120 = 7s
120 = 7s - 4s
120 = 3s
s + 120/3
s = 40 mph is the speed of the freight
then obviously,
40 + 30 = 70 mph is the pass speed
:
:
Check this by finding the dist each traveled
4(70) = 280 mi
7(40) = 280 mi

Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website!
a passenger train leaves the station 3 hours after a freight train left the same station. the freight train travels 30 mph slower than the passenger train. Find the rate of each if the passenger train catches up with the freight train in 4 hours.
**
let x=rate of speed of passenger train
x-30=rate of speed of freight train
Distance=rate of speed*travel time (same for both trains)
travel time for freight train=3+4=7hrs
travel time for passenger train=4hrs (given)
7(x-30)=4x
7x-210=4x
3x=210
x=70
x-30=40
Ans:
rate of speed of passenger train=70 mph
rate of speed of freight train =40 mph

Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website!
Freight Train.
d = r*t
t = 7 hr
r = x mph
.
Passenger Train.
d = r*t
t = 4 hr
r = x+30 mph
.
When the passenger train overtakes the freight train, they will have traveled the same distance, 'd'.
.
d = d
so
7*x = 4*(x+30)
7x = 4x + 120
3x = 120
x = 40 mph = speed of freight train
.
x+30 = 70 = speed of passenger train
.
Do the distance work out?
7 * 40 = 280 miles
4 * 70 = 280 miles
Correct.
.
Done.