Tommy and zach are starting out at the same position. tommy runs north at 5 miles per hour and zach starts to run east 2 hours later at the rate of 8 miles per hour. how long until tommy and zach are 16 miles apart? round to the nearest tenth if necessary.

After 2.90 hours Tommy and Zach will be 16 mils apart

Step-by-step explanation:

Let Tommy and Zach run for t hours until they are 16 miles apart.

Tommy runs North with the speed of 5 miles per hour.

So, distance covered by Tommy in t hours = 5t miles

Zach runs East with the speed of 8 miles per hour.

Since Zach started 2 hours late so he will run for (t - 2) hours.

Distance covered in (t - 2) hours with the speed of 8 miles per hour = 8(t - 2) miles

Now both are 16 miles apart so we will apply Pythagoras theorem in the given triangle.

[8(t - 2)]²+ (5t)² = 16²

64(t - 2)² + 25t² = 256

64(t² + 4 - 4t) + 25t² = 256

64t² + 256 - 256t + 25t² = 256

89t² -256t + 256 - 256 = 0

89t² - 256t = 0

t( 89t - 256) = 0

(89t - 256) = 0

89t = 256

t =

t = 2.90 hours

After 2.90 hours Tommy and Zach will be 16 mils apart.

correct

step-by-step explanation: