A man travels from his home to office at 4km/hr and reaches his office 20 min late. If the Speed had been 6 km/hr he would have reached 10 min early. Find the distance from his home to office?

Question: A man travels from his home to office at 4km/hr and reaches his office 20 min late. If the Speed had been 6 km/hr he would have reached 10 min early. Find the distance from his home to office?

Solution:
Let the distance from home to office = d km

Time taken at 4 km/h = d/4 hours
And time taken at 6 km/h = d/6 hours

The difference between these two times = late time + early time = 20 min + 10 min = 30 min = 1/2 hours

ATQ,
(d/4) - (d/6) = 1/2
⇒ (3d - 2d)/12 = 1/2
⇒ d = 12/2
∴ d = 6 km

So the distance from home to office is 6 km.