ibauguil
contestada

Students have organized
a three-day walkathon to raise money for
charity. The average walking speeds of four
participants are given in the table below.

Walking Speed


Elijah. 3.2
Aubrey. 3
Mercedes. 2.4
Steve. 3.5


Part A Write and solve an inequality to
determine how many hours it would take Steve
to walk at least 21 mi on Day 1


Part B: At the beginning of Day 2, Mercedes
is 2 mi ahead of Elijah. Write and solve an
inequality to determine the hours x when
Elijah will be behind Mercedes.


Part C: At the beginning of Day 3, Elijah starts
walking at the marker for Mile 42, and Aubrey
starts walking at the marker for Mile 42.5.
Write and solve an inequality to determine the
hours when Elijah is ahead of Aubrey.

Respuesta :

frika

Answer:

Part A. At least 6 hours

Part B.  In less than 2.5 hours Elijah will be behind Mercedes

Part C.  In more than 2.5 hours Elijah will be ahead Aubrey

Step-by-step explanation:

D = distance

v =speed

t = time

Formula connecting D, v and t:

[tex]D=v\cdot t[/tex]

Part A.

Steve's speed: [tex]v=3.5\ mph[/tex]

Distance: at least 21 miles

Time: unknown, so

[tex]3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6[/tex]

It would take Steve at least 6 hours to walk at least 21 mi on Day 1.

Part B.

Mercedes's speed: [tex]v_M=2.4\ mph[/tex]

Elijan's speed: [tex]v_E=3.2\ mph[/tex]

Elijan's Distance walked: [tex]D_E[/tex] miles

Mercedes's Distance walked: [tex]D_M[/tex] miles

Time: x hours

Mercedes is 2 miles ahead, so

[tex]D_E=3.2x\\ \\D_M=2.4x+2[/tex]

Elijan will be behind when

[tex]D_E<D_M\\ \\3.2x< 2.4x+2\\ \\3.2x-2.4x<2\\ \\0.8x<2\\ \\8x<20\ [\text{Multiplied by 10}]\\ \\x<\dfrac{20}{8}\\ \\x<2.5\ hours[/tex]

In 2.5 hours Elijan will catch up Mercedes, and in less than 2.5 hours Elijah will be behind Mercedes.

Part C.

Aubrey's speed: [tex]v_M=3\ mph[/tex]

Elijan's speed: [tex]v_E=3.2\ mph[/tex]

Elijan's Distance walked: [tex]D_E[/tex] miles

Aubrey's Distance walked: [tex]D_A[/tex] miles

Time: x hours

At the beginning of Day 3, Elijah starts walking at the marker for Mile 42,  and Aubrey starts walking at the marker for Mile 42.5.

[tex]D_E=42+3.2x\\ \\D_A=42.5+3x[/tex]

Elijan will be ahead of Aubrey when

[tex]D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours[/tex]

In 2.5 hours Elijan will catch up Aubrey, and in more than 2.5 hours Elijah will be ahead Aubrey.

Otras preguntas