Final answer:
After receiving the warning SMS, the friend has 55 seconds to get out of the building. This time is calculated based on the seismic wave traveling 1 km/s and the distances involved in forming a right triangle with the epicenter, the message sender, and the friend's locations.
Step-by-step explanation:
The question requires us to calculate the time available for the friend to get out of a building after receiving a warning SMS about an earthquake. The epicenter is 25 km due south of the message sender and the friend is 60 km due west from the sender. Assuming seismic waves travel at a speed of 1 km/s and it takes 10 seconds to send/read an SMS, first we need to find the distance from the epicenter to the friend's location. This can be done by applying the Pythagorean theorem to the distances, considering them as sides of a right triangle.
The distance from the epicenter (A) to the sender (B) is 25 km and from the sender to the friend (C) is 60 km. The epicenter to the friend forms the hypotenuse (D) of the triangle ABC. So, D^2 = A^2 + C^2, which gives us D^2 = 25^2 + 60^2. Therefore, D = sqrt(25^2+60^2) = sqrt(625+3600) = sqrt(4225) = 65 km.
The seismic waves travel 65 km at 1 km/s speed to reach the friend. So, it will take 65 seconds for the seismic waves to travel from the epicenter to the friend. Subtracting the 10 seconds needed to read the SMS, the friend has 55 seconds to get out of the building after reading the SMS.