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:
Now, we can find the time when the trains will be 1520 km apart:
Where 1 is for the cargo train and 2 is for the passenger train.
Since we need to calculate the time when the trains are 1520 km apart, t₁ = t₂, so:
For the cargo train, it will be 1520 km apart from the passenger train at:
And for a passenger train, it will be 1520 km apart from the cargo train at:
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:
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!