SOLUTION: the lengths of two trains are 220metres,180metres respectively. They overtake together in opposite direction in 16 seconds and they overtake in same direction in 1 minute. find the

Algebra ->  Permutations -> SOLUTION: the lengths of two trains are 220metres,180metres respectively. They overtake together in opposite direction in 16 seconds and they overtake in same direction in 1 minute. find the      Log On


   

Question 891545: the lengths of two trains are 220metres,180metres respectively. They overtake together in opposite direction in 16 seconds and they overtake in same direction in 1 minute. find the speeds of the two trains
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can think of this as one of the trains
moving at either the sum or the difference
of their speeds, and the other train standing
still.
--------------
Let +s%5B1%5D+ = the speed of the faster train
Let +s%5B2%5D+ = the speed of the slower train
--------------
Trains traveling in opposite directions:
(1) +220+%2B+180+=+%28+s%5B1%5D+%2B+s%5B2%5D+%29%2A16+
Trains traveling in same direction:
(2) +220+%2B+180+=+%28+s%5B1%5D+-+s%5B2%5D+%29%2A60+
---------------------------------
In both cases, the length of one train has to
completely pass the length of the other, so
you add the lengths.
It takes longer to pass going in the same
direction, so you subtract the speeds
----------------------------------
(1) +400+%2F16+=+s%5B1%5D+%2B+s%5B2%5D+
(1) +s%5B1%5D+%2B+s%5B2%5D+=+25+
and
(2) +400%2F60+=+s%5B1%5D+-+s%5B2%5D+
(2) +s%5B1%5D+-+s%5B2%5D+=+20%2F3+
------------------------
Add the equations
+2s%5B1%5D+=+95%2F3+
+s%5B1%5D+=+95%2F6+
+s%5B1%5D+=+15.833+
and
(2) +s%5B1%5D+-+s%5B2%5D+=+20%2F3+
(2) +95%2F6+-+s%5B2%5D+=+40%2F6+
(2) +s%5B2%5D+=+55%2F6+
(2) +s%5B2%5D+=+9.166+
The speeds of the trains are 15.833 m/sec
and 9.166 m/sec
---------------------
check:
(1) +400+%2F16+=+s%5B1%5D+%2B+s%5B2%5D+
(1) +400+%2F16+=+15.833+%2B+9.166+
(1) +25+=+25+
and
(2) +s%5B1%5D+-+s%5B2%5D+=+20%2F3+
(2) +15.833+-+9.166+=+6.666+
(2) +6.666+=+6.666+
OK

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
he lengths of two trains are 220metres,180metres respectively.
They overtake together in opposite direction in 16 seconds and
they overtake in same direction in 1 minute.
find the speeds of the two trains
:
let x = speed of the 220 m train in meters/min
let y = speed of the 180 m train " " "
:
Going opposite direction, their speeds are additive
Going the same direction, their relative speed is their difference
:
total distance for the trains to clear each other 220 + 180 = 400 m
:
Write distance equation for each scenario, dist = time * speed
1(x-y) = 400
x - y = 400
and
16%2F60(x + y) = 400
multiply both sides by 60
16(x + y) = 24000
divide both sides by 16
x + y = 1500
:
Use elimination with these two equations
x - y = 400
x + y = 1500
--------------Adding eliminates y find x
2x = 1900
x = 1900/2
x = 950 m/min
Find y
950 + y = 1500
y = 550 m/min
:
Chance these to km/hr for the two trains
%28950%2A60%29%2F1000 = 57 km/hr
%28550%2A60%29%2F1000 = 33 km/hr