Mohan covers a distance of 187 km at the speed of S km/hr. If Mohan increases his speed by 6 km/hr, then he takes 6 hours less. What is the value of S?

Given, Distance = 187 km
Initial Speed = S km/hr
Let Initial time = T hours
Then, ST = 187 km
New speed = (S+6) km/hr
New Time = (T-6) km/hr
Then, (S+6)(T-6) = 187
=> ST - 6S + 6T - 36 = 187
Substituting ST = 187,
=> 187 - 6S + 6T - 36 = 187
=> 6T - 6S = 36
=> T - S = 6
Substituting T = $$\dfrac{187}{S}$$,
$$\dfrac{187}{S} - S = 6$$
=> $$\dfrac{187 - S^2}{S} = 6$$
=> $$S^2 + 6S - 187 = 0$$
=> $$S^2-11S+17S-187 = 0$$
=> $$S(S-11)+17(S-11) = 0$$
=> $$(S-11)(S+17) = 0$$
S = 11 or S = -17
Speed cannot be negative.
Hence, Speed of Mohan = 11 km/hr