Select the correct answer from the following choices i, ii, iii or iv
i) 1⅓ hours
ii) 2 hours
iii) 4 hours
iv) 6 hours
Solution:
Let the volume of the bath tub be v m3
Let the rate of flow of the cold water tap be x m3/ h
Let the rate of flow of the hot water tap be y m3/ h
Let the time taken by the cold water tap to fill the tub be z hours
Using the cold water tap alone,
Volume, v = xz m3
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPpx9_xHk1KGkT2nf9H2uH3rCFSXYY8uVMN9eI0A32Gs-MyICVOr2hutibsVZR096PiRAEcM2BDeCWFefLD4OqKiM4wHlcIyD0UUyLwQfNwP0V_Y7EV4Q9aq7p8I5MGnomLLhDLsylMDUj/s400/Cold+water+flow+rate,+x.jpg)
Using the hot water tap alone,
Volume, v = y(z + 2) m3
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdV8nnZtrSSfQFRBDDxHFYa7biA4xWq9HB7y7pv4eWChQmuBAWI0cL_VU65CkNZYAD3H-qCGpCvFemLf8mf6cxYlWpjXk_BBhab1UeKZmteidToKM0y12Ivt65HufQUbvdWAzAUXaW1ILd/s400/Hot+water+flow+rate,+y.jpg)
Using both water taps at the same time,
Volume, v = (x + y)( 1⅓) m3 since 1 hour 20 minutes is 1⅓ hours
Substituting x and y into the equation,
v=(x + y)( 1⅓)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP1Lyuj_qwipj86c7XZPLlIsqphm1SJ9-30YnCZfKnRR8-6zUbGevBiUbRWPrJyCRncrB-peccTlGXfKKgXjwGWLciE7bMGQmMnQaHCWAcKd-rLm7pWemSO80VqVJDJjS1Qm6ccXoYFgED/s400/Solving+equation.jpg)
4(2z+2)=3z(z+2)
8z+8=3z2+6z
3z2-2z-8=0
(3z+4)(z-2)=0
Solving for z,
z = 2 or
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgP0Gsd_4MA_APXfWuHEcJp8bL1yRbM_FPepiuBWsdvX2KQx3NZZUhuy1gcLBMlPvEgV26v0EN6UwvX1XBIgJTEu0KDCGr8e1dFtkdbkOOOlEV62xEASj2RiETJTv0SJxZ7OkqkHi2Lk9rV/s400/z,+invalid+solution.jpg)
Therefore, time taken by the cold water tap to fill the tub is 2 hours
And time taken by hot water tap is 2 + 2 = 4 hours
The answer is (iii).
Reference
- Hey Math! assignment (E-Maths), July 2010, Question #5, Revision Paper