Answer:
The time were the two trains are closest together is 10:35:41
Step-by-step explanation:
Here we are given;
Train A: Speed = 100 km/h
Direction = North or y axis
Departure time = 10:00
Train B: = Speed = 120 km/h
Direction = West or x axis
Departure time = 11:00
Therefore, we have;
Distance of separation, d between the two trains is given as follows
d(t)² = (100·t)² + (120 - 120·t)²
d(t) = √((100·t)² + (120 - 120·t)²) = √(24400·t²-28800·t+14400)
Differentiating and equating to zero, we have;
[tex]20\cdot \frac{61 \cdot 2\cdot t -72}{2\cdot \sqrt{61.2\cdot t^{2}-72\cdot t+36}} = 0[/tex]
Cross multiplying we have;
61×2×t -72 = 0
Which gives t = 36/61 hours = 35.41 mins after Train A starts the journey or 10:35:41 ≈ 10:36.
