SOLUTION: A train and a car are 180km apart. If they travel towards each other, they will meet in 50 minutes. If they travel in the same direction, the train will overtake the car in 1.8 hou

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A train and a car are 180km apart. If they travel towards each other, they will meet in 50 minutes. If they travel in the same direction, the train will overtake the car in 1.8 hou      Log On


   

Question 1025576: A train and a car are 180km apart. If they travel towards each other, they will meet in 50 minutes. If they travel in the same direction, the train will overtake the car in 1.8 hours. What is the speed of the train?
Found 3 solutions by mananth, josmiceli, stanbon:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
A train and a car are 180km apart. If they travel towards each other, they will meet in 50 minutes. If they travel in the same direction, the train will overtake the car in 1.8 hours. What is the speed of the train?


A train and a car are 180km apart.
let speed of train be x
and car be y
moving towards time = 50/60 = 5/6 hour
t=d/r
5/6 = 180/(x+y)
5x+5y= 1080
x+y= 216...........(1)
t If they travel in the same direction,
the catch up time is 1.8 hours
catchup speed = (x-y)
180/(x-y) = 1.8 = 9/5
9x-9y= 900
x-y = 100..................(2)
add (1) &(2)
2x = 316
x= 158
Train speed = 158 km/h
So car speed = 158-100=58 km/h

the train will overtake the car in 1.8 hours. What is the speed of the train?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The train can overtake the car only
if it is faster than the car, so it
definitely must be faster
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Let +s%5Bc%5D+ = the speed of the car in km/hr
Let +s%5Bt%5D+ = the speed of the train in km/hr
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When they travel towards eachother, think of
one of them standing still and the other
moving at the sum of their speeds
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Moving towards eachother:
+180+=+%28+s%5Bt%5D+%2B+s%5Bc%5D+%29%2A%285%2F6%29+
+s%5Bt%5D+%2B+s%5Bc%5D+=+%286%2F5%29%2A180+
(1) +s%5Bt%5D+%2B+s%5Bc%5D+=+216+
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When they travel in the same direction,
subtract the speeds. The car has a +180+ km
head start.
In +1.8+ hrs, the car travels +s%5Bc%5D%2A1.8+ km
The train travels +s%5Bt%5D%2A1.8+ km
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I can say:
+s%5Bt%5D%2A1.8+=+s%5Bc%5D%2A1.8+%2B+180+
++s%5Bt%5D%2A1.8+-+s%5Bc%5D%2A1.8+=+180+
+1.8%2A%28+s%5Bt%5D+-+s%5Bc%5D+%29+=+180+
(2) +s%5Bt%5D+-+s%5Bc%5D+=+100+
---------------------
Add the equations
(1) +s%5Bt%5D+%2B+s%5Bc%5D+=+216+
(2) +s%5Bt%5D+-+s%5Bc%5D+=+100+
---------------------
+2s%5Bt%5D+=+316+
+s%5Bt%5D+=+158+
and
(1) +s%5Bt%5D+%2B+s%5Bc%5D+=+216+
(1) +158+%2B+s%5Bc%5D+=+216+
(1) +s%5Bc%5D+=+58+
-----------------------
The speed of the train is 158 km/hr
check:
+180+=+%28+s%5Bt%5D+%2B+s%5Bc%5D+%29%2A%285%2F6%29+
+180+=+%28+158+%2B+58+%29%2A%285%2F6%29+
+%286%2F5%29%2A180+=+216+
+1080+=+5%2A216+
+1080+=+1080+
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A train and a car are 180km apart. If they travel towards each other, they will meet in 50 minutes. If they travel in the same direction, the train will overtake the car in 1.8 hours. What is the speed of the train?
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The sum of their rate is 180km/(5/6)hr = 216 kph
So t+c = 216 kph
-----
train distance = 180+x km
car distance = x km
-----
train rate = (180+x)/1.8 kph
car rate = x/1.8 kph
-------
Equation:
(180+x + x)/1.8 = 216
(180+2x)/1.8 = 216
------
180+2x = 388.8
2x = 208
x = 104 km
train distance = 104 + 180 = 284 km
Ans: train rate = 284/1.8 = 157.78 kph
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Cheers,
Stan H.
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