If a man walks 1 km/hr faster than his usual speed then he covers a distance of 3 km in 15 minutes less time. Find his usual speed.

Explanation

Let the usual speed of the man be x km/hr.
Time taken to cover 3 km at usual speed `=(3)/(x)` hours.
Actual speed to the man `=(x+1)km/hr.`
Time taken to cover 3 km at actual speed `=(3)/((x+1))` hours.
`:." "(3)/(x)-(3)/((x+1))=(15)/(60)implies(3)/(x)-(3)/((x+1))=(1)/(4)`
`implies" "(1)/(x)-(1)/((x+1))=(1)/(12)implies((x+1)-x)/(x(x+1))=(1)/(12)`
`implies" "(1)/((x^(2)+x))=(1)/(12)impliesx^(2)+x-12=0`
`implies" "x^(2)+4x-3x-12=0impliesx(x+4)-3(x+4)=0`
`implies" "(x+4)(x-3)=0impliesx+4=0" or "x-3=0`
`implies" "x=-4" or "x=3impliesx=3" "[because" speed cannot be negative"]`
Hence, the usual speed of the man is 3 km/hr.