Question

A hot air balloon begins ascending at a rate of 18 feet per minute. A second hot air balloon begins ascending 2 minutes later at a rate of 27 feet per minute. How many minutes will it take for the second hot air balloon to catch the first hot air balloon?

a) 4 minutes
b) 6 minutes
c) 8 minutes
d) 10 minutes

Answer 1

It will take 4 minutes for the second hot air balloon to catch the first hot air balloon.

Step-by-step explanation:

To find how long it will take for the second hot air balloon to catch the first, we need to determine the time it takes for the two balloons to reach the same altitude.

Let's assume that it takes the second balloon t minutes to catch the first balloon. After 2 minutes, the first balloon has already ascended 2 * 18 = 36 feet. At that time, the second balloon is at the same altitude and begins ascending at a faster rate of 27 feet per minute. So, the equation for the distance traveled by the second balloon is 27t + 36.

Since both balloons are traveling the same distance, we can set up an equation:

18t = 27t + 36

27t - 18t = 36

9t = 36

t = 4

Therefore, it will take 4 minutes for the second hot air balloon to catch the first hot air balloon.