The transmitter site of radio station WGGW and the

transmitter site of another radio station, WGWB, are
on the same highway 100 miles apart. The radio signal
from the transmitter site of WGWB can be received
only within a radius of 60 miles in all directions from
the WGWB transmitter site. For how many miles along
the highway can the radio signals of both stations be
received?
(Note: Assume the highway is straight.)

To determine how many miles along the highway the radio signals of both stations can be received, we need to identify the overlapping area of the coverage circle for each station.

First, let's visually represent the scenario. Imagine a straight line representing the highway, with two points on it, one for the WGGW transmitter site and the other for the WGWB transmitter site. The radius of the coverage area for WGWB is 60 miles in all directions from its site.

Now, consider that the distance between the two transmitter sites is 100 miles. Since the WGWB coverage area is a circle with a radius of 60 miles around its site, the coverage area extends 60 miles in each direction from the WGWB site along the highway. Therefore, the total length of WGWB's coverage along the highway is 60 + 60 = 120 miles.

However, we also need to account for the fact that the two stations are 100 miles apart. This means that the coverage area of WGWB will not reach the entire distance between the two transmitter sites.

To find the overlapping area along the highway, we need to consider two scenarios:

1. If the distance between the two sites is less than or equal to 120 miles (twice the radius of WGWB's coverage), then the entire length between the two sites will be covered by WGWB.
2. If the distance between the two sites is greater than 120 miles, then the overlapping area will be less than the total length covered by WGWB.

In this case, since the distance between the two sites is 100 miles (less than 120 miles), the radio signals of both stations can be received along the entire distance of the highway, which is 100 miles.

Therefore, the radio signals of both stations can be received for 100 miles along the highway.