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Variation - Joint - more examp...
The time, t, take to buy fuel at a petrol station varies directly as the number of vehicles, v, in the queue and inversely as the number of pumps, p, available in the station. In a station, with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find
the number of pumps required to fuel 36 vehicles in 15 minutes.

Correct Answer

Incorrect Answer

How to get the right answer:

v = number of vehicles in the queue.
p = number of pumps in the station.
From the joint variation, we know that
t = kv / p where when t = 10 and v = 20, p = 5
10 = k x 20 / 5
10 x 5 = k x 20
k = 10 x 5 / 20 = 5 / 2
The relation between t, p and v is therefore t = 5v/2p
When v = 36 and t = 15 minutes,
15 = 5 x 36 / 2p
P = 5 x 36 / 2 x 15 = 6 pumps