Question

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 48 minutes less. What is the speed of the train?

• A. 35 km/h
• B. 45 km/h
• C. 40 km/h
• D. 50 km/h

Answer 1

The Correct Option is B

Let the original speed be \( x \) km/h.
Then, time taken = \( \frac{360}{x} \) hours.

New speed = \( x + 5 \) km/h.
New time = \( \frac{360}{x + 5} \) hours.

According to the question:
\[ \frac{360}{x} - \frac{360}{x+5} = \frac{48}{60} = 0.8 \]
Multiply through by \( x(x+5) \):
\[ 360(x+5) - 360x = 0.8x(x+5) \]
\[ 360x + 1800 - 360x = 0.8x^2 + 4x \Rightarrow 1800 = 0.8x^2 + 4x \]
Multiply entire equation by 10 to remove decimal:
\[ 18000 = 8x^2 + 40x \Rightarrow 8x^2 + 40x - 18000 = 0 \Rightarrow x^2 + 5x - 2250 = 0 \]
Solve using quadratic formula:
\[ x = \frac{-5 \pm \sqrt{5^2 + 4 \cdot 2250}}{2} = \frac{-5 \pm \sqrt{9025}}{2} = \frac{-5 \pm 95}{2} \]
\[ x = \frac{90}{2} = 45 \quad \text{(negative value ignored)} \]

Check with \( x = 45 \):
Time = \( \frac{360}{45} = 8 \) hours
New time = \( \frac{360}{50} = 7.2 \) hours
Difference = \( 0.8 \) hours = 48 minutes.

Answer is \(\boxed{45 \text{ km/h}}\).