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SAT Math 2.3 Algebra and Functions. Calculate this function.
SAT Math: Calculating Heating Time Using Proportion and Equations 7 Views
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Description:
When placed in a glass beaker on a hot plate at a moderate temperature, 5 milliliters of water heats up at a rate of 8 °C per second. The amount of time it takes to heat water increases linearly when heating greater amounts of water. Eduardo needs to boil 300 milliliters of water for a chemistry experiment. How many minutes would he need to wait for the water to reach its boiling point of 100 °C, given that the water's initial temperature is 25°C? Round your answer to the nearest tenth.
Transcript
- 00:01
Arch members knew section same grid thing here with the
- 00:06
circles squares and triangles in the little dunce cap here
- 00:09
right at the bottom I used to wear that a
- 00:11
lot All right here we go men Last play at
- 00:14
a moderate temperature Five milliliters water heats up at a
Full Transcript
- 00:16
rate of degrees centigrade for second amount of time It
- 00:18
takes to keep water increases linearly when he'd in greater
- 00:19
amount of water and water With these guys you're about
- 00:21
one hundred meters of water for chemistry That's What you
- 00:23
need to wait for the water to reach it's boiling
- 00:24
point one hundred grand larceny attempted to raise your answer
- 00:26
in your hand right We're going up seventy five degrees
- 00:30
here from twenty five to one hundred boiling point and
- 00:33
it's increasing at eight degrees centigrade per second Arithmetically Meaning
- 00:37
steadily not geometrically or some other weird combo thing So
- 00:41
how do we think about this Well if you're not
- 00:43
a science fan pour you pretend that eduardo is actually
- 00:46
trying to make soup or coffee or whatever parade for
- 00:49
practice still applications Yet you too could be a barista
- 00:52
someday five milliliters of water rises eight degrees centigrade in
- 00:55
one second Since the problems says that heating time increases
- 01:00
leaning yearly with greater amounts of water While set up
- 01:03
a proportion to see how long it takes for three
- 01:05
hundred milliliters they heat up eight degrees centigrade it right
- 01:08
We have five milliliters is one second So three hundred
- 01:11
millilitres is how many seconds Well yeah It's a minute
- 01:13
Right Five over One three hundred over x Yeah The
- 01:16
expression tells us that three hundred million litres of water
- 01:18
heats up eight degrees centigrade in sixty seconds What a
- 01:21
convenient cohen kid ink Sixty seconds is one minute and
- 01:24
the problem wants the answer in minutes Who Who We
- 01:27
can say that two Hundred million litres of water heats
- 01:29
at eight degrees per minute Now we need to cook
- 01:32
up an equation to see how long it takes to
- 01:34
cook up the water Well the water temperature rises at
- 01:36
eight degrees centigrade a minute So this value is the
- 01:39
slope right there that represent the final temperature is sea
- 01:42
in the number of minutes of eating time is t
- 01:45
so c equals eight t one more thing The water's
- 01:48
already at twenty five degrees If it were zero well
- 01:51
we'd be playing around with ice Great for a hot
- 01:54
summer day Not great for a problem like this to
- 01:57
account for the water's initial temperature at twenty five is
- 01:59
the why in earth except in the equation Yeah just
- 02:02
c equals eighty plus twenty five hundred that's are boiling
- 02:06
point Their equals eighty plus twenty five track t from
- 02:10
outside to get seventy five equals eighteen Divide ate both
- 02:13
sides And while you get about nine point four Well
- 02:15
eduardo needs to wait nine point four minutes for that
- 02:18
soup or coffee or chemistry experiment Tio a boil Maybe
- 02:22
he can boil some tea while he waits Yeah Put
- 02:24
that hot water to use
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