Final answer:
Ursula will take a total of 3.5 hours, or 3 1/2 hours, to reach her destination by rowing across a river for 2 hours and then running the remaining 21 km for 1.5 hours.
Step-by-step explanation:
The question asks for the total time Ursula takes to reach her destination by rowing across a river and then running along the shore.
Firstly, we must determine the distance Ursula rows diagonally across the river to reach a point that is 6 km downshore. To do this, we can use the Pythagorean theorem. If we let x represent the distance rowed, then:
x2 = 82 + 62
x2 = 64 + 36
x2 = 100
x = 10 km
Next, we will calculate the time it takes to row this distance.
Time to row = distance/speed
Time to row = 10 km / 5 km/h
Time to row = 2 hours
After reaching the opposite shore, Ursula runs the remaining 21 km (27 km - 6 km).
Time to run = distance/speed
Time to run = 21 km / 14 km/h
Time to run = 1.5 hours
Finally, we combine the times:
Total time = Time to row + Time to run
Total time = 2 hours + 1.5 hours
Total time = 3.5 hours
Ursula will reach her destination in 3.5 hours, which can be expressed as 3 hours and 30 minutes, or as a mixed number, 3 1/2 hours.