Question

The total distance an object travels varies directly with the length of time it travels. If an object travels 24 meters in 9 seconds, how long will it take to travel 96 meters?

Answer 1

Answer: it will take 36 seconds to travel 96 meters.

Explanation:

Let d represent the total distance that the object travels.

Let t represent the length of time that the object travels.

The total distance an object travels varies directly with the length of time it travels. This means that

d is directly proportional to t

Introducing a constant vof proportionality k, it becomes

d = kt

If an object travels 24 meters in 9 seconds, then

24 = k × 9

k = 24/9

The expression becomes

d = 24t/9

Therefore, the time it will it take to travel 96 meters would be

96 = 24t/9

t = 96 × 9/24

t = 36 seconds

Answer 2

It takes 36 seconds for the object to travel 96 meters.

Explanation:

We are given the following in the question:

The total distance an object travels varies directly with the length of time it travels.

An object travels 24 meters in 9 seconds.

Speed of object =

`\text{Speed} = \frac{\text{Distance}}{\etext{Time}}\\\\=(24)/(9) = (8)/(3)\text{ meters per second}`

Now, we have to calculate the time taken to travel by the object for 96 meters.

`\text{Time} = \frac{\text{Distance}}{\text{Speed}}`

Putting the values, we get,

`\text{Time} = (96)/((8)/(3)) = (96* 3)/(8) = 36\text{ Seconds}`

Thus, it takes 36 seconds for the object to travel 96 meters.