Question

Monika is running around a park on a trail that is 7 miles long. The number of mile Monika has run, d, after t minutes is modeled by the equation shown.

d= 1/15t + 1

Mark is running around the same trail and starts at the same time as Monika. His speed is 3/4 as fast as Monika's speed, and he starts a mile behind her.
Graph the equation that models Mark's run at this speed.

Answer 1

$d = \frac{1}{15}t + 1 \\ \\ 1. \: d = \frac{t}{15} + 1 \\ 2. \: d -1 = \frac{t}{15} \\ 3. \: (d - 1) \times 15 = t \\ 4. \: 15(d - 1) = t \\ 5. \: t = 15(d - 1)$

Answer 2

The Mark's distance equation is given as (3÷4)×(1÷15t + 1).

• Concept of speed, distance & time.

    Speed: Speed is defined as the rate of distance covered per unit time.

So, Speed = distance÷time

The units of speed can be determined by knowing the units of distance and time.

Example, In this question distance is in miles so unit of speed will be miles per second,or it can be miles per minute or miles per hour depending on the unit of time.

Monica's speed can be defined as  d÷t as the formula of speed is distance over time

so Monica's speed  = 1÷15$t^{2}$ + 1÷t

According to question,Mark is running at 3÷4th speed of Monica

So Mark's speed = (3÷4)×(1÷15t²+1÷t)

so,the distance covered by Mark will be Mark's speed × time

Distance covered = (3÷4)×(1÷15t²+1÷t)×t

⇒(3÷4)×(1÷15t + 1)

Learn more about speed,distance & time here,

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