Transcript The Taco Cart Inquiry Problem

• We predicted that Ben will get to the Taco
Cart first. This was based on assuming the
speed travelled on the street was not double
that of the speed travelled on sand.
• Other information which was crucial to
determine a more definitive answer was:
– Speed travelled on both sand and street.
– Dimensions of the beach (length to taco cart
directly, length to street and length from street
to taco cart)
• This information allows us to make a far more
accurate guess since we can now solve for
time for both individuals
a. Ben:
𝑑
650.026 𝑓𝑡
𝑡= =
= 325.013𝑠 = 𝟓 𝐦𝐢𝐧 𝟐𝟓 𝒔
𝑠
2 𝑓𝑡/𝑠
b. Mr. Singh:
𝑑 325.6 𝑓𝑡 562.6 𝑓𝑡
𝑡= =
+
= 275.32𝑠
𝑠
2 𝑓𝑡/𝑠
5 𝑓𝑡/𝑠
= 𝟒 𝐦𝐢𝐧 𝟑𝟓. 𝟑𝟐𝟎𝒔
Part II
Determine the exact position of the cart on
the road such that both Ben and Me will
reach it at the exact same time.
Determine the distances Ben and Me would
have to walk individually and their individual
times.
- Graphically
- Algebraically
Algebraically
Step 1: Determine functions that represent the
time taken to walk to the taco cart for each
person.
- Time taken for Ben: distance(m) / 2(m/s)
- (√a² + 325.6²) / 2
- Time taken for Mr. Singh: distance(m) / 5(m/s)
- 325.6(m) / 5 (m/s) + a(m) / 5 (m/s)
T= c/2 + x/5
X= 562.6-b
Algebraically
Step 2: Set the functions of time together to
find the distance required from the taco cart to
the left side of the triangle.
- √(a² + 325.6²) / 2 = 325.6/5 + a/5
Step 3: Solve for a.
a = 0 ft and 318.05 ft.
If the taco bar is placed at 0 ft or 318.5 ft from
the left side of the road, then it will both Mr.
Singh and Ben the same time to walk.
Graphically
• Step 1:
-Using desmos punch in y = √(a²
+ 325.6²) / 2 and y= 325.6/5 +
a/5
This is because they are the
functions.
Graphically
• Step 2: Solve for a.
-Using desmos, punch in y = √(b² + 325.6²) / 2 +562.6-b/5 + a/5
Find abs. min because, it shows the distance of x when time is minimum
Pa rt I I I
D i a g ra m w i t h rel eva nt eq u at i o n s
b
325.6 ft.
c
a
562.6 ft.
650.03 ft.
Taco Cart
Minimum (fastest) time to Taco Cart
Determined Algebraically
Minimum (fastest) time to Taco Cart
Determined Graphically
Minimum (fastest) time to Taco Cart
Determined Numerically
Part IV
• We enjoyed working algebraically and graphically most
of the time as it allowed us to be creative and create
equations to solve the problems.
• Numerically was our least favourite as it was the most
tedious
• Desmos was very useful as it allowed us to see visually
what was happening and found the abs. min with ease
• This assignment allowed us to experience the power
and accuracy of desmos and graphs. We learned the
relationships between algebra and graphing.
• This let us experience how calculus can be applied to
real life situations.