Mandy is skating at 5 miles per hour . nikki is skating at 6 miles per hour and started 1 mile behind mandy. if their rates stay the same will mandy catch up with nikki? explain.

Answer,

YES, if their rates stay the same, Nikki will catch up with Mandy in 1 hour

EXPLANATION

Mandy’s speed is 5 miles per hour

Distance covered = Speed * time

Mandy’s distance covered at time, t = 5t

Therefore, her position at time t = 5t

Nikki’s speed is 6 miles per hour

Distance covered = Speed * time

Nikki’s distance covered at time, t = 6t

Since Nikki started 1 mile behind Mandy, her position at time t = 6t - 1

If Nikki will catch up with Mandy, then there must be a real value for t, t which both Nikki and Mandy are at the same position

Testing if there is a real value for t where, 5t = 6t – 1

5t = 6t – 1

6t – 1 = 5t

Add 1 to both sides of the equation

6t – 1+ 1 = 5t + 1

6t = 5t + 1

Subtract 5t from both sides of the equation

6t – 5t = 5t – 5t + 1

t = 1

1 is a real value; this means after they have both skated for 1 hour Nikki will catch up with Mandy.

the answer is 37

step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: