Question

12. A large reaction vessel is filled with water. In the morning X m' are added to the vessel. More water is added to fill the vessel in the afternoon. Water is added for Y hours at a rate of Z m°/minute a. Write an algebraic expression for T, the total amount of liquid the reaction vessel can take. Show your working/ reasons (in words or using mathematics).

b. If 20,000 m° is pumped in during the morning. Lt takes 6 hours to complete filling the vessel in the afternoon at a rate of 1000 m°/minute, what is the capacity of the reaction vessel in m°?

Answer 1

(a) Let the total amount of water filled the vessel be $T$

Amount of water filled in the morning = $Xm$^o

Time taken to fill the vessel in the afternoon$=Y hours$

Time taken to fill the vessel in the afternoon in minutes$=(Y hrs \times60)minutes=60Yminutes$

Rate$=Zm$^o$/minute$

Total amount of water filled in the afternoon$=Zm$^o$/minute$$\times60Yminutes=60YZm$^o

Hence the algebraic expression;$T=Xm$^o$+60YZm$^o

(b)Amount of water filled in the morning$=20000m$^o

Rate$=1000m$^o$/minute$

Time taken to fill the vessel in the afternoon$=6 hours$

Using algebraic expression;$T=Xm$^o$+60YZm$^o

$T=20000m$^o$+(60\times6\times1000)m$^o

$T=20000m$^o$+360000m$^o

$T=380000m$^o