Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)
Answer: 12 km/hr
Let the speed be \(x\) km/hr. Time \(= \dfrac{48}{x}\) hours; with faster speed, time \(= \dfrac{48}{x + 4}\) hours.
\(\dfrac{48}{x} - \dfrac{48}{x + 4} = 1\)
\(\dfrac{48(x + 4) - 48x}{x(x + 4)} = 1 \Rightarrow \dfrac{192}{x^2 + 4x} = 1\)
\(x^2 + 4x - 192 = 0\)
\((x + 16)(x - 12) = 0\)
\(x = 12\) (speed cannot be negative).
Check: \(48 \div 12 = 4\) h, \(48 \div 16 = 3\) h; difference 1 h ✓.