Two high-speed trains begin travelling toward each other from stations Alpha and Beta, which are separated by a distance of 210 km. Train A departs from Alpha at 7:00 a.m. moving at a constant speed of 25 km/h. Train B departs from Beta at 8:00 a.m. and the two trains pass each other at 11:00 a.m. Determine the speed of Train B in km/h (rounded to two decimal places).

The correct option is 36.67 km/h.

Step 1: Calculate the total time traveled by Train A
Train A departs from Station Alpha at 7:00 a.m. and meets Train B at 11:00 a.m.

$\text{Time for Train A}=11:00\text{a.m.}-7:00\text{a.m.}=4\text{hours}$

Step 2: Calculate the distance traveled by Train A
Using the distance formula:

$\text{Distance covered by Train A}=\text{Speed of Train A}\times \text{Time for Train A}$

$\text{Distance covered by Train A}=25\text{km/h}\times 4\text{hours}=100\text{km}$

Step 3: Calculate the distance covered by Train B
The total distance separating station Alpha and station Beta is 210 km. Since both trains travel towards each other until they meet, the sum of their distances equals the total distance. Therefore:

$\text{Distance covered by Train B}=\text{Total distance}-\text{Distance covered by Train A}$

$\text{Distance covered by Train B}=210\text{km}-100\text{km}=110\text{km}$

Step 4: Calculate the time traveled by Train B
Train B departs from Station Beta at 8:00 a.m. and meets Train A at 11:00 a.m.

$\text{Time for Train B}=11:00\text{a.m.}-8:00\text{a.m.}=3\text{hours}$

Step 5: Determine the speed of Train B
Now, divide the distance traveled by Train B by the time it was moving:

$\text{Speed of Train B}=\frac{\text{Distance covered by Train B}}{\text{Time for Train B}}$

$\text{Speed of Train B}=\frac{110\text{km}}{3\text{hours}}\approx 36.6667\text{km/h}$

Rounding to two decimal places gives:

$\text{Speed of Train B}=36.67\text{km/h}$