Question

a plate moving at a rate of 3 cm/year is moving toward a plate that is 1,500 km away. in how many years will the plates collide?
○ 50,000,000 years
○ 50,000 years
○ 5,000 years
○ 500 years

Explanation:

Step1: Convert units to be consistent

First, we need to convert the speed from cm/year to km/year. We know that 1 km = 100000 cm (since 1 km = 1000 m and 1 m = 100 cm, so \(1\times1000\times100 = 100000\) cm). So a speed of 3 cm/year is equal to \(\frac{3}{100000}\) km/year.

Step2: Use the formula \(time=\frac{distance}{speed}\)

The distance between the plates is 1500 km. The speed \(v=\frac{3}{100000}\) km/year. Using the formula \(t=\frac{d}{v}\), we substitute \(d = 1500\) km and \(v=\frac{3}{100000}\) km/year. So \(t=\frac{1500}{\frac{3}{100000}}\). When dividing by a fraction, we multiply by its reciprocal, so \(t = 1500\times\frac{100000}{3}\).

Step3: Calculate the time

First, simplify \(1500\div3 = 500\). Then multiply by 100000: \(500\times100000=50000000\)? Wait, no, wait. Wait, maybe there was a typo in the problem? Wait, maybe the speed is 3 cm/year, but maybe the intended speed is 3 cm/year, but let's re - check. Wait, 1500 km is 150000000 cm (since 1 km = 100000 cm, so 1500×100000 = 150000000 cm). Then time \(t=\frac{distance}{speed}=\frac{150000000\ cm}{3\ cm/year}=50000000\) years? But that's not one of the options. Wait, maybe the speed is 3 cm/year is wrong, maybe it's 3 cm/year is 3 km/year? No, that doesn't make sense. Wait, maybe the distance is 1500 km, and speed is 3 cm/year. Wait, 3 cm/year is 0.00003 km/year. Then time is 1500 / 0.00003=50000000 years. But the options have 50,000,000? Wait, the first option is 50,000,000 years? Wait, maybe I misread the options. Let me check again. The options are: 50,000,000 years; 50,000 years; 5,000 years; 500 years. Wait, maybe the speed is 3 cm/year is 30 cm/year? No, wait, maybe the problem has a typo, but assuming the speed is 3 cm/year and distance is 1500 km (150000000 cm), then time is 150000000 / 3 = 50000000 years, which is 50,000,000 years.

Answer:

50,000,000 years (the first option)