Suppose the tanker is heading due south.

When the tanker contacts the coast guard, it is out of range (110 > 90)

We need to find out how far west of the station the tanker is, and how far north it is.

The angle the line between the tanker and the station makes with the east-west line is 45 degrees = pi/4

So the tanker is cos(pi/4) x 110 = 77.78km west of the station and sin(pi/4) x 110 = 77.78km north of the station (it is exactly north-west of the station, so this makes sense)

The tanker comes in to radar range when the line between the tanker and the station is 90km long. It stays the same distance west of the station, as it is heading due south, so it will be

sqrt(90^2 - 77.78^2) = 45.28km north of the station when it comes in to range.

It will stay in range until it is 45.28km south of the station (using symmetry). So it will be in range for

45.28*2 = 90.55km

At a speed of 25km/h this will take 90.55/25 = 3.62 hrs = **3hrs 37 mins**

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