Question

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?

• A. 45 km/h
• B. 60 km/h
• C. 72 km/h
• D. 40 km/h

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 $t_2$.

Answer 1

The Correct Option is B

Let the speed of the first train be $s_1$ km/h.
Let the speed of the second train be $s_2 = 90$ km/h.
Both trains travel the same distance: $d = 360$ 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, then time = $360 / 45 = 8$ hours. Time difference = $8 - 4 = 4$ hours. Matches the condition.
Final Answer: \[ \boxed{45 \text{ km/h}} \]