Question

Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until Tommy and Zach are 8 miles apart?

Answer 1

Answer:

2.56 hr

Step-by-step explanation:

Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until Tommy and Zach are 8 miles apart?

Let say After T hrs when Tommy Starts then they are 8 miles apart

Tommy after T hrs  = 3T  miles  North

Zach After T - 2 Hrs = 4(T - 2)  Miles East

Distance between them = √( (3T)²  + (4(T -2))² )

=>√( (3T)²  + (4(T -2))² )  = 8

Squaring both sides

=> 9T² + 16(T - 2)² = 64

=> 9T² + 16(T² + 4 - 4T) = 64

=> 9T² + 16T² +64 - 64T = 64

=> 25T² - 64T = 0

=> 25T - 64 = 0

=> T = 64/25

=> T = 2.56 hr

2.56 hrs until Tommy and Zach are 8 miles apart