the volume of a small balloon is 2 liters and a larger balloon is 5 liters. the small balloon is increased at a rate of 0.3 per sec. larger balloon is decreased at a rate of 0.12 liters per sec. after how many seconds will the two balloon have the same liters.
let the time taken be t seconds
2 + .3t = 5 - .12t
.42t = 3
t = 3/.42 = 7.14 seconds
check:
after 7.14 seconds, volume of smaller balloon = 2 + 7.14(.3) = 4.14
after 7.14 seconds, volume larger ballon = 5 - 7.14(.12) = 4.14
OK then!
To find out when the two balloons will have the same volume, we can set up an equation based on the given information:
Let's say t represents the number of seconds it takes for the two balloons to have the same volume.
The volume of the small balloon is given by:
V_small = 2 + 0.3t
The volume of the larger balloon is given by:
V_large = 5 - 0.12t
To find when the two volumes are equal, we set them equal to each other and solve for t:
2 + 0.3t = 5 - 0.12t
Let's simplify the equation:
0.3t + 0.12t = 5 - 2
0.42t = 3
t = 3 / 0.42
t ≈ 7.14
Therefore, after approximately 7.14 seconds, the two balloons will have the same volume.