To determine if Tommy will make it to his cousin's house in time, we can use the Pythagorean theorem to calculate the distance between Tommy's house and his cousin's house.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, Tommy's house, his cousin's house, and the Irvine Spectrum form a right triangle. Tommy's house is 12 miles north of the Spectrum, and his cousin's house is 9 miles east of the Spectrum.
Let \(d\) be the distance between Tommy's house and his cousin's house. Then, according to the Pythagorean theorem:
\[d^2 = 12^2 + 9^2\]
\[d^2 = 144 + 81\]
\[d^2 = 225\]
\[d = \sqrt{225}\]
\[d = 15\]
So, the distance between Tommy's house and his cousin's house is 15 miles.
Tommy rides his bike at a rate of 5 minutes per mile. Therefore, to travel 15 miles, he will take \(15 \times 5 = 75\) minutes.
Since Tommy only has 50 minutes to get to his cousin's house, he will not make it in time. He will need 75 minutes to travel the 15 miles, which exceeds the 50 minutes he has available.
Hope this helps!
