Answer:
a) The trains will be 1520 km apart at 2:40 pm for the cargo train and at 4:40 pm for the passenger train.
b) At that time the cargo train has traveled 560.04 km and the passenger train has traveled 960.12 km.
Step-by-step explanation:
a) First, we need to find the distance traveled by the cargo train in the two hours before the passenger train leaves Chicago:
[tex] x_{1} = v_{1}t_{1} = 120 km/h*2h = 240 km [/tex]
Now, we can find the time when the trains will be 1520 km apart:
[tex] 1520 km = (x_{1} + 240 km) + x_{2} [/tex]
Where 1 is for the cargo train and 2 is for the passenger train.
[tex] 1520 km = (v_{1}*t_{1} + 240 km) + v_{2}t_{2} [/tex]
Since we need to calculate the time when the trains are 1520 km apart, t₁ = t₂, so:
[tex] 1520 km = (v_{1}*t + 240 km) + v_{2}t [/tex]
[tex]t = \frac{1520 km - 240 km}{120 km/h + 360 km/h} = 2.667h[/tex]
For the cargo train, it will be 1520 km apart from the passenger train at:
[tex]t_{1} = 12 pm + 2 h + 40 min = 2:40 pm[/tex]
And for a passenger train, it will be 1520 km apart from the cargo train at:
[tex]t_{2} = 2 pm + 2 h + 40 min = 4:40 pm[/tex]
Hence, the trains will be 1520 km apart at 2:40 pm for the cargo train and at 4:40 pm for the passenger train.
b) The distance traveled by both trains is given by:
[tex] x_{1} = v_{1}*t + 240 km = 120 km/h*2.667 h + 240 km = 560.04 km [/tex]
[tex] x_{2} = v_{2}*t = 360 km/h*2.667 h = 960.12 km [/tex]
Therefore, at that time the cargo train has traveled 560.04 km and the passenger train has traveled 960.12 km.
I hope it helps you!
