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?

it will take Zach 2 hrs to get 8 miles because he is running at a constant of 4

while tommy is running at a constant of 3 it will take him 3 and a half hrs to run 8 miles

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slicergiza slicergiza · Answer 2 · 2019-07-26T06:38:26-04:00

Answer:

\(\frac{14}{25}\) hours.

Step-by-step explanation:

We know that,

Distance = speed × time

Given,

Speed of tommy = 3 miles per hour,

So, the distance covered by him 2 hours = 6 miles,

Also, speed of Zach = 4 miles per hour,

Let after x hours they are 8 miles apart,

That is, total distance covered by Tommy = 6 + 3x,

And, total distance covered by Zach = 4x,

Thus, by making the diagram of this situation,

We get,

A right triangle having hypotenuse 8 and legs 3x+6 and 4x,

By the pythagorean theorem,

\((3x+6)^2+(4x)^2=8^2\)

\(9x^2+36x+36+16x^2=64\)

\(25x^2+36x-28=0\)

\(25x^2+50x-14x-28=0\)

\(25x(x+2)-14(x+2)=0\)

\((25x-14)(x+2)=0\)

\(25x-14=0\text{ or }x+2=0\)

⇒ x = \(\frac{14}{25}\) or x = -2

Number of hours can not be negative,

Hence, after \(\frac{14}{25}\) hours they are 8 miles apart.