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Two pipes running together can fill a cistern in minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
Let one pipe fills a cistern in x mins.
Other pipe fills the cistern in (x + 3) mins.
Running together can fill a cistern in minutes = 40/13 mins
Part filled by one pipe in 1min =
Part filled by other pipe in 1min =
Part filled by both pipes Running together in 1min =
13x2 + 39x = 80x + 120
13x2 – 41x – 120 = 0
Using the splitting middle term – the middle term of the general equation is divided in two such values that:
Product = a.c
For the given equation a = 13 b = – 41 c = – 120
= 13. – 120 = – 1560
And either of their sum or difference = b
= – 41
Thus the two terms are – 65 and 24
Difference = – 65 + 24 = – 41
Product = – 65.24 = – 1560
13x2 – 65x + 24x – 120 = 0
13x(x – 5) + 24(x – 5) = 0
(x – 5) (13x + 24) = 0
(x – 5) = 0 (13x + 24) = 0
x = 5 or x = – 24/13
x = 5 (speed cannot be negative fraction)
Hence one pipe fills a cistern in 5 minutes and other pipe fills the cistern in (5 + 3) = 8 minutes.
While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed of the plane. Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?