A daily commuter usually reaches his office on time by driving at a speed of 40 km/hr. One day, due to traffic, he drives at 30 km/hr and reaches 20 minutes late. What is the distance to his office?
40 km
Let the distance to office be \(d\) km.
Usual time = \(\tfrac{d}{40}\) hours; slower time = \(\tfrac{d}{30}\) hours.
Extra time = 20 minutes = \(\tfrac{1}{3}\) hour, so \(\tfrac{d}{30}-\tfrac{d}{40}=\tfrac{1}{3}\).
\(\dfrac{4d-3d}{120}=\dfrac{1}{3}\Rightarrow \dfrac{d}{120}=\dfrac{1}{3}\Rightarrow d = 40\) km.
Hence, the distance to his office is 40 km.
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