A train crosses a $1000\text{ m}$ long bridge in $52\text{ seconds}$ and another $700\text{ m}$ long bridge in $40\text{ seconds}$. Assuming the train is running at a uniform speed, what is the speed (in km/h) of the train?

Let the length of the train be $L$ meters and its uniform speed be $v$ m/s.When a train crosses a bridge, the total distance traveled is equal to the sum of the length of the train and the length of the bridge.From the first case:
$${\text{Distance}}_1=L+1000=v\times 52⟹L=52v-1000\text{— (Equation 1)}$$
From the second case:
$${\text{Distance}}_2=L+700=v\times 40⟹L=40v-700\text{— (Equation 2)}$$
Equating Equation 1 and Equation 2:
$$52v-1000=40v-700$$
$$52v-40v=1000-700$$
$$12v=300$$
$$v=\frac{300}{12}=25\text{ m/s}$$
Convert the speed from m/s to km/h:
$$\text{Speed}=25\times \frac{18}{5}=5\times 18=90\text{ km/h}$$