Answer:
The first siding should be located at 30 miles
The time for the freight to arrive at the siding is 40 minutes
Step-by-step explanation:
From the given information:
Let [tex]T_f[/tex] represent the time for the freight train
Also, let [tex]T_P[/tex] represent the time at which the passenger train reach the location
Let Y represents the location where the location of the siding of the track needed to take place.
Thus, for freight time:
[tex]T_f = \dfrac{Y}{45} --- (1)[/tex]
The siding location is:
[tex]T_P = \dfrac{2}{6}+\dfrac{Y}{70}[/tex]
[tex]T_P =0.333+\dfrac{Y}{70} --- (2)[/tex]
To determine Y:
[tex]T_P -T_f = 0.1 --- (3)[/tex]
replacing the value of [tex]T_f[/tex] and [tex]T_P[/tex] in the above equation (3), we have:
[tex]0.333+\dfrac{Y}{70} - \dfrac{Y}{45} =0.1[/tex]
collecting like terms, we have:
[tex]\dfrac{Y}{70} - \dfrac{Y}{45} =0.1-0.333[/tex]
[tex]\dfrac{45Y- 70Y}{3150} =-0.233[/tex]
[tex]\dfrac{-25Y}{3150} =-0.233[/tex]
- 25Y = -0.233 × 3150
- 25Y = -733.95
Y = -733.95/-25
Y = 29.36 miles
Y [tex]\simeq[/tex] 30 miles to the nearest whole number
Thus, the first siding should be located at 30 miles
To estimate the time for the fight to arrive the siding, we replace 30 miles for [tex]T_f[/tex] in equation (1).
Then, we have:
[tex]T_f = \dfrac{Y}{45}[/tex]
[tex]T_f = \dfrac{30}{45}[/tex]
[tex]T_f =0.667\ hr[/tex]
[tex]T_f =(0.667 \times 60 )minutes[/tex]
[tex]T_f =40.2 \ minutes[/tex]
[tex]\mathsf{T_f \simeq 40 \ minutes}[/tex]
Thus, the time for the freight to arrive at the siding is 40 minutes
