Kelly realizes once she gets to Round Rock that she left her Art project (a major grade) at her mother's house in Plano. She would not have time to have it shipped
before it is due the next day and convinces her brother to meet her part of the way. If
the average speed limit from Plano to their meeting point (on the North side of West,
TX) is 65 miles per hour, and the average speed limit from Round Rock to their meeting
point is 75 miles per hour, how many miles will Kelly's brother have to drive before he
reaches Kelly if the driving distance between them is 196 miles and they drive the same
amount of time?

Kelly's brother has to drive 91 miles before he reaches Kelly.

Step-by-step explanation:

Since, both Kelly and her brother are traveling at the constant speed. Therefore, we will use the following formula for both:

s = v t

For Kelly:

s₁ = v₁ t₁

t₁ = s₁/v₁   equation 1

where,

t₁ = time taken by Kelly

s₁ = distance covered by Kelly

v₁ = average speed of Kelly = 75 mi/h

For Brother:

s₂ = v₂ t₂

t₂ = s₂/v₂   equation 2

where,

t₂ = time taken by Brother

s₂ = distance covered by Brother

v₂ = average speed of Brother = 65 mi/h

But it is given that both of them drive same amount of the time:

t₁ = t₂

using equation 1 and equation 2:

s₁/v₁ = s₂/v₂

s₁/s₂ = v₁/v₂

using values:

s₁/s₂ = (75 mi/h)/(65 mi/h)

s₁/s₂ = 1.15

s₁ = 1.15 s₂   equation 3

The total distance is given as:

s₁ + s₂ = 196 miles  

using equation 3:

1.15 s₂ + s₂ = 196 miles

s₂ = 196 miles/2.15

s₂ = 91 miles

Hence, Kelly's brother has to drive 91 miles before he reaches Kelly.