11-06-2005, 09:37 PM
A cow was standing on a bridge, 5feet away from the middle of the bridge. suddenly a lightning
express with 90 miles/hr was
coming towards the bridge from nearest end of the cow.seeeing this the cow ran towards the
express and managed to escape
when the
train is one feet away from the bridge. if it would have ran to opposite direction
(ie away from train) it would have been
hit the train one ft away from the end of the bridge.
Calculate the length of bridge.:grab:
Solution:
Suppose that the length of the bridge is 'd' units and the train is at a distance x units from one end of the bridge and hence (x + d) units from the other end.
If the speed of the cow is v, then according to the ptoblem, we have:
(x - 1)/90 = {(d/2) - 5}/v ---------- (1)
and
(d + x + 1)/90 = {(d/2) + 5 - 1}/v ---------- (2)
Dividing (2) by (1), we get:
(d + x + 1)/(x - 1) = {(d/2) + 4}/{(d/2) - 5}
On simplification, we get:
d^2 - 8d - (18x + 2) = 0
Solving for d, we get:
d = 4 + square root of (18x + 18 )
For x = 1, we get d = 10
For x = 7, we get d = 16
For x = 17, we get d = 22
For x = 71, we get d = 40
.......... and so on.