Calculate Relative Speed

Since both trains are traveling in the same direction, their relative speed is the difference between their individual speeds: $v_{rel} = 40 - 22 = 18 \text{ km/h}$.

$v_{rel} = 40 - 22 = 18 \text{ km/h}$

Convert Speed to m/s

Convert the relative speed from km/h to m/s by multiplying by $\frac{5}{18}$: $18 \times \frac{5}{18} = 5 \text{ m/s}$.

$18 \times \frac{5}{18} = 5 \text{ m/s}$

Calculate Total Distance Covered

The total distance covered to cross each other completely is the sum of the lengths of both trains ($l_1 + l_2$). Time taken is $1 \text{ minute} = 60 \text{ seconds}$. Therefore, $\text{Total Distance} = 5 \text{ m/s} \times 60 \text{ s} = 300 \text{ m}$.

$\text{Total Distance} = 5 \times 60 = 300 \text{ m}$

Find Length of Second Train

Given that the length of the first train ($l_1$) is $125 \text{ m}$, we can find the second train's length ($l_2$): $125 + l_2 = 300 \implies l_2 = 300 - 125 = 175 \text{ m}$.

$l_2 = 300 - 125 = 175 \text{ m}$