A train traveling at a uniform speed passes a 455 meter long platform in 17 seconds and another platform. 175 meter long in 10 seconds. find the length and speed of the train.
Answers
Answer:
Given, 3x
2
+5x+2=0
On comparing this equation with ax
2
+bx+c=0, we get a=3,b=5 and c=2
Now, b
2
−4ac=(5)
2
−4×3×2
=25=24
=1
x=
2a
−b±
b
2
−4ac
==
2×3
−5±
1
=
6
−5±1
x=
6
−5+1
x=
6
−5−1
∴
3
−2
and −1 are the roots of the given quadratic equation.
Let the speed of the train be 's' m\sec
and length of train be 'L' m.
Given Equation: Bridge of distance 275 m and time is 15 seconds.
Bridge of distance 425 m and time is 21 seconds.
Factor to consider is length of Train.
Hence total length =Bridge length+Length of train
According to the formula:
Speed =
Time
Distance
Equation 1 . s =
15
L+275
Similarly for equation 2. s=
21
L+425
From Equation 1 and Equation 2.
15
L+275
=
21
L+425
21×(L+275)=15×(L+425)
21×L+21×275=15×L+15×425
6×L=600
L=100 m.
To calculate speed of train Substitute value of L in equation 1 or equation 2.
Equation 1.
s=
15
L+275
s=
15
100+275
= 25 m\s
To calculate speed in km\hr.
1km = 1000 m
1 hr = 3600 sec
1 m\sec =
1000
3600
=
5
18
25 m\sec =25×(
5
18
) km\hr
= 90 km\hr