A train leaves a station at 10:00 and travels due North at a speed of 100km/h. Another train has been heading due west at 120km/h and reaches the same station at 11:00. At what time were the two trains closest together?

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;

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.

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6