Question

The height to which a balloon with hydrogen gas rises in the air varies directly as time. Given table has some observations about the time and the corresponding height of the balloon (in meters). Find the missing term in the table.

Time (in minutes)	3	4	--	25	--
Height of a balloon (in meters)	--	48	84	--	1860

Answer 1

Hint: Here, we will first take the division of the column where both the values are given. Then we use the obtained solution to find the rest of the places to complete the given table.

Complete step-by-step answer:

Given that when the time is 4 min, then the height is 48 meters.

We will find the height of a balloon in the air when time is 1 min by dividing the height of 48 meters by the time given.

\[\dfrac{{48}}{4} = 12{\text{ meters}}\]

We will now find the height of a balloon in the air when time is 3 minutes from the above value.

\[3 \times 12 = 36{\text{ meters}}\]

Again we will use the above value of 12 meters to find the height of a balloon in the air when time is 25 minutes.

\[25 \times 12 = 300{\text{ meters}}\]

We know that when the height is 48 meters, then the time is 4 min.

We will now find the minutes the balloon takes to be at height 1 meter in the air by dividing the 4 min by the height given.

\[\dfrac{4}{{48}} = \dfrac{1}{{12}}{\text{ min}}\]


We will now find the time a balloon takes to be at height 84 meters in the air from the above value.

\[84 \times \dfrac{1}{{12}} = 7{\text{ min}}\]


Again we will use the above value of \[\dfrac{1}{{12}}\] minutes to find the time a balloon takes to be at the height of 1860 meters in the air.

\[1860 \times \dfrac{1}{{12}} = 155{\text{ min}}\]

Therefore, we will now use the above values to fill the missing places of the given table.

Time (in minutes)	3	4	7	25	155
Height of a balloon (in meters)	36	48	84	300	1860

Note: In solving these types of questions, we will use the table for the accuracy of the solution and one must check the units of the given values. Some students divide the value of height in meters by the time to find the value of 1 min, which is wrong. Students should also write the values carefully to avoid calculation mistakes.