Regarding the starting time in the question, Miss Loi actually meant it to be from the point the phone call is made (hence the word *initial* in the question). But having reread the question, she found that this can be open to different interpretation so she should just state this clearly the next time :P.

In any case, it'll still overflow regardless!

]]>Most Rate of Change questions in your Ten-Year Series are quite kind to state explicitly the variables involved and their relationship i.e. `y` = f(`x`)

But others, like this one, requires you to *read* the question carefully to determine the variables and their relationship.

1) So from the question, you're supposed to find the rate of change of the *height* (`h`) of the water level i.e.

2) But you're given that the *width* of the water level (`w`) is lengthening *constantly*, which means you can obtain by simply

3) But from the Chain Rule we'll still need to form the expression for the relationship between `h` and `w` in order to obtain .

So ...

See the two little right-angled triangles formed at the sides?

Taking one of this triangles to form the following similarity ratio, can you see that:

So at any given time, the water level `w` can be expressed by:

---- (1)

and viola we have you relationship between `h` and `w`!

So

which is exactly the same answer as **Someone**'s!

Which means that the height of the water is rising at 2 cm per minute, and in 50 mins it would have risen by 50 x 2 = 100 cm.

And since it's given that the initial width is 60cm, from (1)

⇒ initial height = (60-50) x 2 = 20 cm

⇒ height = (20 + 100) cm = 120 cm in 50 mins!

⇒ OVERFLOW!

⇒ It was REALLY scary driving the car through the flood! Miss Loi felt like she was driving a boat!

]]>Considering the full triangle, with x as the 'chopped off' length, by similar triangles,

w is the width at any particular time, by similar triangles,

In 50 minutes, the water will have risen by another ~~25cm~~ 100cm; from an initial ,

To give a final height of ~~40+25=65 cm; which is less than 100~~

40+2(50)=140>100,

overflows

Once again Miss Loi has inserted a diagram for readers to better understand your solution - especially on the whereabouts of your 'chopped-off length' `x` ðŸ˜› For your solution Miss Loi was just about to pounce on you until she saw your next comment!

The Chain Rule and similar triangles are definitely required to solve this Rate of Change question (**Papillion**'s epic shortcut nowithstanding) ðŸ˜› ðŸ˜› ðŸ˜›

Miss Loi's similar triangles are a little different - though the final answer is the same, but once again it's great to be able to highlight that there's often more than one way to solve the same question ðŸ˜€

Miss Loi's solution coming right up ...

P.S. Thought the initial water level width was 60cm (not 70cm)? Hence initial `h` = 2(60)-100 = 20. CARELESS MISTAKE! Tsk tsk.

My bad my bad ... in her neverending quest for the dramatic, Miss Loi was too complacent to see this obvious shortcut coming from the blindside ðŸ™‚

Guess you already know that this is a question on *Rate of Change*, so she should better rephrase to the following:

Find the rate at which the height of the water in the drain is rising, and *hence* determine if the height of the water in the drain will overflow within 50 mins.

Oh and with the weather these days, please don't even predict how the rain will behave!

Bring on your **Chains**!

Here it goes:

Let x be the width of the water level, with 60cm as the starting and 100cm being the max level. Assume that the change of x with respect to time is constant (though it's weird...cos it means that the rain must be getting progressively heavier and heavier, not exactly what I can imagine when the meteorological station says that the rain will stop in 50 mins time...oh well)

60 to 70 cm takes 10 min

70 to 80 cm takes 10 min

80 to 90 cm takes 10 min

90 to 100 cm takes 10 min

In total, it'll take 40 mins for x to reach 100 cm. Another longer than that, the water will over flow out.

My spidey sense is tingling...so Miss Loi pls point out any wrong assumptions I've made, thks!

]]>But by simply dividing the change in *area* (`A`) (which is in another dimension) by 10 mins you are implying that is also constant.

Are you absolutely sure?

]]>