Secondary 4 Rate of Flow (Hey Math)

From: Hey Math! assignment (E-Maths), July 2010, Question #5, Revision Paper

A rectangular shaped bath tub can be filled with water flowing from two taps in 1 hour and 20 minutes. If the cold water tap alone takes 2 hours less than the hot water tap to fill the bath tub, find the time taken in hours by the hot water tap to fill the bath tub.

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



Using the hot water tap alone,
Volume, v = y(z + 2) m³



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)

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



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

Secondary 4 Circle and trigonometry (Hey Math)

From: Hey Math! assignment (E-Maths), July 2010, Question #7, Circle and trigonometry

An arc which subtends and angle of 60° at O is shown below. Find the ratio of r : R.



Select the correct answer from the following choices.
i) 1 : 2
ii) 1 : √2
iii) 1 : √3
iv) 1 : 3


Solutions:

With reference to the following diagram;



The radius ABO passed through the center of the circle ARC and bisects the angle EOD.
Triangle BCO is a right angled triangle with angles 30°, 60° and 90°.

By trigonometry,
if BC = r, then BO = 2r.

Therefore radius of the arc DAE = AB + BO = 3r
Given that the radius of the arc DAE = R,
That is, R = 3r
Therefore the ratio of r : R is 1 : 3.

The answer is (iv).


Reference

• Hey Math! assignment (E-Maths), July 2010, Question #7, Circle and trigonometry