Final answer:
Sue Chin can paddle out a distance of 2 km into the lake before she must return to make it back within 1.5 hours, considering her speeds of 2 km/h paddling out and 4 km/h returning.
Step-by-step explanation:
The situation presented is a classic problem that deals with average speed and time. We know that Sue Chin has 1.5 hours to both paddle out into a lake and return. We are also given her speeds for paddling out and returning, which are 2 km/h and 4 km/h, respectively. Since she has to spend equal time paddling out and coming back to meet her 1.5-hour deadline, we can use the harmonic mean formula to find the average speed for the entire trip.
The harmonic mean (H) of two speeds A and B, when the time traveled at each speed is the same, is given by H = 2AB / (A + B). Substituting in the values given (A = 2 km/h and B = 4 km/h), we get H = 2(2)(4) / (2 + 4) = 16 / 6 = 2.67 km/h as the average speed for the round trip.
Since the total trip time is 1.5 hours, we can find the total distance covered by multiplying the average speed by the total time, which gives us a distance of D = 2.67 km/h * 1.5 hours = 4 km. Since this is the round trip distance, Sue can paddle out 2 km (half of the total distance) before having to return.