3. Three town \( P, Q \) and \( R \) arcen the parallel of latitude 20 N The distance between \( P \) and \( Q \) is 1482 kilometres and between \( Q \) and \( R \) is 926 kilometers \( Q \), whose congitude is \( 10^{\circ} \) is is between \( P \) and \( R \). Find tee longitude of \( P \) and \( R \)

To find the longitudes of towns \( P \) and \( R \), let's first understand that the Earth is divided into 360 degrees of longitude. At the latitude of \( 20^\circ N \), each degree of longitude covers a smaller distance than at the equator due to the curvature of the Earth. At \( 20^\circ N \), the distance per degree of longitude is approximately 1,874 kilometers. Now, given that the distance between \( P \) and \( Q \) is 1482 kilometers and between \( Q \) and \( R \) is 926 kilometers, we can calculate the longitudes: 1. For the distance between \( P \) and \( Q \): \[ \text{Degrees of longitude from } P \text{ to } Q = \frac{1482}{1874} \approx 0.79 \text{ degrees} \] Since \( Q \) is at \( 10^\circ \) longitude, \( P \) must be: \[ \text{Longitude of } P = 10 - 0.79 \approx 9.21^\circ \] 2. For the distance between \( Q \) and \( R \): \[ \text{Degrees of longitude from } Q \text{ to } R = \frac{926}{1874} \approx 0.49 \text{ degrees} \] Thus, the longitude of \( R \) is: \[ \text{Longitude of } R = 10 + 0.49 \approx 10.49^\circ \] Therefore, the final longitudes are approximately \( P \) at \( 9.21^\circ \) and \( R \) at \( 10.49^\circ \).