# Chris and Josh have received walkie-talkies for Christmas. If they leave from the same point at the same time, Chris walking north at 2.5 mph and Josh walking east at 3 mph, how long will they be able to tlak to each other if the range of the walkie talkies is 4 miles? Round your answer to the nearest minute.

The distance between them is the hypotenuse of a right triangle. The legs of the triangle are the distances that they travel:
Chris: Y = 2.5 t
Josh: X = 3.0 t, if t is in hours and X and Y are in miles.
When they are 4 miles apart
4^2 = X^2 + Y^2 = [(2.5)^2 + (3.0^2] ^2
16 = 15.25 t^2
t^2 = 1.049 hr^2
t = 1.024 hours = 61 minutes

## To find out how long Chris and Josh will be able to talk to each other, we can use the Pythagorean theorem to determine the distance between them.

Let's assume they start at point O. Chris walks north at a speed of 2.5 mph, so his distance from the starting point after time t is given by Y = 2.5t.

Josh walks east at a speed of 3 mph, so his distance from the starting point after time t is given by X = 3t.

The distance between them is the hypotenuse of a right triangle, where the legs of the triangle are the distances they travel, X and Y.

Using the Pythagorean theorem, we have:

Distance^2 = X^2 + Y^2

Substituting the values we have:

4^2 = (3t)^2 + (2.5t)^2

Simplifying the equation:

16 = 9t^2 + 6.25t^2

Combining like terms:

16 = 15.25t^2

Dividing both sides by 15.25:

t^2 = 16/15.25

t^2 ≈ 1.049

Taking the square root of both sides:

t ≈ √1.049

t ≈ 1.024 hours

To round the answer to the nearest minute, we multiply the decimal part of the hour by 60:

0.024 * 60 ≈ 1.44 minutes

Therefore, Chris and Josh will be able to talk to each other for approximately 1 hour and 1 minute, rounded to the nearest minute.