A school laboratory tank initially contains water at a height of

MATHEMATICS · Multi-part · CBSE · Mathematics · Algebra Play · Algebra Play

Problem

7\,\text{cm}

. After the outlet tap is opened, the height of the water (in centimetres) after

t

minutes is given by the linear polynomial

h(t)=7-0.6t

. (i) Find the time when the tank becomes empty. (ii) The flow rate is changed so that the water level now follows

H(t)=7-kt

and the tank is required to become empty exactly after

9

minutes. Determine the value of

k

. (iii) For the value of

k

obtained in part (ii), verify by direct substitution that

H(t)=0

when

t=9

minutes.