If a train travels 360 km at a uniform speed and takes 4 hours more than another train that travels the same distance at 90 km/h, what is the speed of the first train?
Show Hint
Let speed of first train be $v_1$, time $t_1$. Let speed of second train be $v_2$, time $t_2$.
Distance $d=360$ km. $v_2 = 90$ km/h.
Calculate $t_2 = d/v_2$.
Use the given relation $t_1 = t_2 + 4$.
Calculate $v_1 = d/t_1$.
Read the problem statement carefully to establish the relationship between $t_1$ and $t_2$.
Let the speed of the first train be $s_1$ km/h. The speed of the second train is $s_2 = 90$ km/h. Both trains travel a distance of $d = 360$ km.
Time taken by the second train:
\[
t_2 = \frac{360}{90} = 4 \text{ hours}
\]
The first train takes 4 hours more than the second:
\[
t_1 = t_2 + 4 = 4 + 4 = 8 \text{ hours}
\]
Speed of the first train:
\[
s_1 = \frac{360}{8} = 45 \text{ km/h}
\]
Verification:
If $s_1 = 45$ km/h, the time taken is $360 / 45 = 8$ hours.
The time difference is $8 - 4 = 4$ hours, which matches the given condition.
Final Answer:
\[
\boxed{45 \text{ km/h}}
\]