Step 1 :First, we need to find the rate of ascent of the balloon in meters per second. This can be done by dividing the total distance climbed (71 meters) by the total time taken (40 seconds), which gives us \(\frac{71}{40} = 1.775\) meters per second.
Step 2 :Next, we need to find out how long it would take for the balloon to climb 1 kilometer (or 1000 meters) at this rate. This can be done by dividing the total distance to be climbed (1000 meters) by the rate of ascent, which gives us \(\frac{1000}{1.775} = 563.3802816901409\) seconds.
Step 3 :Finally, since the question asks for the time in minutes, we need to convert the time from seconds to minutes by dividing by 60, which gives us \(\frac{563.3802816901409}{60} = 9.4\) minutes.
Step 4 :Final Answer: The time it will take for the balloon to climb to an altitude of 1 kilometer is approximately \(\boxed{9.4}\) minutes.