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, use the difference in time equation and solve the resulting quadratic.

Answer 1

The Correct Option is A

- Step 1: Let the speed be $S$ km/h. Time taken = $\dfrac{360}{S}$ hours.
- Step 2: With speed $S + 5$, time = $\dfrac{360}{S + 5}$, which is 1 hour less: $\dfrac{360}{S} - \dfrac{360}{S + 5} = 1$.
- Step 3: Simplify: $360 \left( \dfrac{1}{S} - \dfrac{1}{S + 5} \right) = 1$, so $\dfrac{360 \cdot 5}{S(S + 5)} = 1$, $S(S + 5) = 1800$.
- Step 4: Solve quadratic: $S^2 + 5S - 1800 = 0$. Discriminant = $25 + 7200 = 7225$, $S = \dfrac{-5 \pm 85}{2} = 40$ or $-45$. Take $S = 40$.
- Step 5: Verify: At 40 km/h, time = $\dfrac{360}{40} = 9$ hours. At 45 km/h, time = $\dfrac{360}{45} = 8$ hours. Difference = 1 hour.
- Step 6: Check options: Option (a) is 40 km/h, which matches.