Theory question 101
VariationThe time (t) taken to buy fuel at a filling station varies directly as the number of vehicles (V) in a queue and varies inversely as the number of pumps (P), available at the station. In a station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find the: (a) relationship between t, P and V; (b) time it takes to fuel 50 vechicles at a station with 2 pumps; (c) number of pumps required to fuel 40 vehicles in 20 minutes.
Show the model answer
Model answer
(a) t = kV/P; 10 = 20k/5 ⇒ k = 2.5, so t = 2.5V/P (= 5V/2P)
(b) t = 2.5 × 50 ÷ 2 = 62.5 minutes
(c) 20 = 2.5 × 40 ÷ P ⇒ P = 5 pumps
Explanation
Joint variation: V goes on top, P underneath.