Question

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 1

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.