Real-Life Math -- Solution
First, determine how long it takes the robot to mix a bowl of dough.
Mixing
time per bowl = 50 stirs x 1 minute
Mixing time per bowl = 50 minutes
Then
add the time that each bowl is delayed by (more ingredients need to be added
for each new batch of dough).
Delay = 15 minutes
Total mixing
time per bowl = 15 minutes + 50 minutes
Total mixing time per bowl = 65
minutes
Now you need to determine how many bowls can be stirred
in an 8-hour shift.
Total bowls stirred = (8 hours x 60 minutes
per hour) / 65 minutes per bowl
Total bowls stirred = 480 minutes / 65
minutes per bowl
Total bowls stirred = 7.4
The robot can stir
7.4 bowls of cookie dough in an 8-hour shift. This is an increase over the
4 bowls of dough that were previously being stirred without the robot.
Cookies
= 7.4 bowls x 25 dozen cookies per bowl
Cookies = 185 dozen
Because
each bowl holds enough dough for 25 dozen cookies, the robot is currently
stirring enough dough to make 185 dozen cookies.
Increase in production
= 185 dozen cookies - 100 dozen cookies
Increase in production = 85 dozen
cookies
The robot has helped increase production by 85 dozen cookies.
Math skills are extremely important, says robotics engineer Kjerstin Williams.
"There's a whole lot of math out there that you don't even get a
hint of until college," says Williams. "And that's a lot of the math that
we use. So if math isn't quite your thing in high school, a lot of times that
can have a lot to do with rapport with the teachers and the way the curriculum
is presented and that sort of thing.
"I think if in high school you
find that you're kind of OK with trig and kind of OK with calculus but you
really love computer programming, I don't think you should necessarily come
away with this idea that, 'I'm just not that good at math,'" Williams adds.
"Because there's a certain kind of analytical thinking that goes along with
being good at computer programming that bodes well for more advanced mathematical
studies."
Robotics engineers use a lot of statistics and probability.
If you don't like studying that kind of stuff at first, don't give up.
"That
stuff didn't really hold any charm for me and just seemed like a lot of drudgery
until I actually applied it to a real-world problem and saw it do something
for me," says Williams. "The great thing about robotics is, you make something
and you can see it sort of come to life and actually move... When I first
solved a tough robotics problem using some theory from probability and statistics,
holy smokes, all of a sudden I loved probability and statistics. It was like
the coolest thing ever."