To determine how long it will take for the polar bear to catch up to the ice floe, we can start by analyzing their speeds and the initial distance between them.
- Speed of the Ice Floe: 2 km/h
- Speed of the Polar Bear: 10 km/h
- Initial Distance: 7 km
The polar bear is attempting to close the gap between itself and the ice floe. To find out how fast the polar bear is closing that gap, we need to calculate the relative speed between the polar bear and the ice floe:
\[ \text{Relative Speed} = \text{Speed of Polar Bear} - \text{Speed of Ice Floe} = 10 , \text{km/h} - 2 , \text{km/h} = 8 , \text{km/h} \]
Now that we have the relative speed, we can calculate how long it will take for the bear to catch up since it is 7 km away:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{7 , \text{km}}{8 , \text{km/h}} = 0.875 , \text{hours} \]
To convert hours into minutes, we multiply by 60:
\[ 0.875 , \text{hours} \times 60 , \text{minutes/hour} = 52.5 , \text{minutes} \]
Thus, it will take the polar bear approximately 52 and a half minutes to catch up to the ice floe. If rounding is required, it would be rounded to 53 minutes.