Final answer:
Noah can build a tower at the rate of 4/5 feet per 4/9 hour. To find the time it would take for him to build a 9-foot-tall tower, a proportion is set up and solved, yielding a result of 1.25 hours.
Step-by-step explanation:
The student has provided the rate at which Noah can build a tower: 4/5 feet in 4/9 of an hour. To calculate the time it takes to build a 9 feet tall tower, we use the following ratio:
Time to build 4/5 feet: Time to build 9 feet = 4/9 hours: x hours
By setting this up as a proportion, we get (4/5) / (4/9) = 9 / x
Cross multiplying gives us 4x = (9 * 4/9) * 5 which simplifies to 4x = 5
Dividing both sides by 4, we obtain x = 5/4 or 1.25 hours as the time it takes Noah to build a 9-foot-tall tower.