Question

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less. What is the speed of the train?

• A. 40 km/h
• B. 45 km/h
• C. 50 km/h
• D. 55 km/h

Hint:

For speed-time problems, set up equations based on time difference and solve the resulting quadratic.

Answer 1

The Correct Option is A

- Step 1: Let the speed be $s$ km/h, time taken = $\frac{360}{s}$ hours.
- Step 2: With speed $s + 5$, time taken = $\frac{360}{s + 5}$, which is 1 hour less: $\frac{360}{s} - \frac{360}{s + 5} = 1$.
- Step 3: Simplify: $360 \left( \frac{1}{s} - \frac{1}{s + 5} \right) = 1 \implies 360 \left( \frac{s + 5 - s}{s(s + 5)} \right) = 1 \implies \frac{360 \times 5}{s(s + 5)} = 1$.
- Step 4: So, $s(s + 5) = 1800 \implies s^2 + 5s - 1800 = 0$.
- Step 5: Solve quadratic: $s = \frac{-5 \pm \sqrt{25 + 7200}}{2} = \frac{-5 \pm 85}{2}$, so $s = 40$ or $s = -45$ (discard negative).
- Step 6: Verify: At $s = 40$, time = $\frac{360}{40} = 9$ hours; at $s = 45$, time = $\frac{360}{45} = 8$ hours, difference is 1 hour. Option (1) is correct.