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Train A is going 40 miles per hour down a 160-mile track. Train A started down the track at 6:30. Train B is going down another 245-mile track at 85 miles per hour. If there is an intersection 43 miles down Track A and 68 miles down Track B, when would train B have to depart for the two trains to collide?

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To determine when Train B must depart so that both trains collide at the intersection, we can follow these steps:

  1. Calculate when Train A reaches the intersection.

    Train A travels at a speed of 40 miles per hour and needs to cover 43 miles to reach the intersection.

    \[ \text{Time for Train A to reach intersection} = \frac{43 \text{ miles}}{40 \text{ mph}} = 1.075 \text{ hours} \approx 1 \text{ hour and } 4.5 \text{ minutes} \]

    Since Train A started at 6:30:

    \[ 6:30 + 1 \text{ hour } 4.5 \text{ minutes} = 7:34:30 \]

    Therefore, Train A will reach the intersection at approximately 7:34:30.

  2. Calculate when Train B needs to reach the intersection.

    Train B, traveling at 85 miles per hour, needs to cover 68 miles to reach its intersection.

    \[ \text{Time for Train B to reach intersection} = \frac{68 \text{ miles}}{85 \text{ mph}} = 0.8 \text{ hours} \approx 48 \text{ minutes} \]

    Since Train A will reach the intersection at 7:34:30, Train B needs to arrive at the intersection at the same time. We need to find what time Train B must depart to reach the intersection by 7:34:30:

    \[ \text{Departure time for Train B} = 7:34:30 - 0.8 \text{ hours} = 7:34:30 - 48 \text{ minutes} = 6:46:30 \]

Thus, Train B must depart at approximately 6:46:30 for the two trains to collide at the intersection.