Let, v represent the speed of the bus and t represent the time required to travel from one town to the other.
The speed of the bus varies inversely with the time required to travel from one town to the other.
∴ v ∝ 1/t
∴ v = k x (1/t)
where, k is the constant of variation.
∴ v × t = k …(i)
It takes 5 hours to travel from one town to the other if speed of the bus is 48 km/hr. i.e., when v = 48, t = 5
∴ Substituting v = 48 and t = 5 in (i), we get v × t = k
∴ 48 × 5 = k
∴ k = 240
Substituting k = 240 in (i), we get v × t = k
∴ v × t = 240 …(ii)
Since, the speed of the bus is reduced by 8 km/hr,
∴ Speed of the bus in second case (v) = 48 – 8 = 40 km/hr
∴ When v = 40, t = ?
∴ Substituting v = 40 in (ii), we get v × t = 240
∴ 40 × t = 240
∴ t = 240/40
t = 6
∴ The problem is of inverse variation and the bus would take 6 hours to travel the distance if its speed is reduced by 8 km/hr.
