Question

Tyshawn observes a marble travel along a horizontal path at a constant rate. The marble travels one third 3 1 ​ of the length of the path in 3, one quarter3 4 1 ​ seconds. At that rate, how many seconds does it take the object to travel the full length?

Answer 1

11/4 seconds to travel the full length of the path.

Explanation:

To solve this problem, we can use the following formula:

distance = rate × time

Let’s assume that the length of the path is L.

According to the problem statement, the marble travels one third (1/3) of the length of the path in 3 seconds. Therefore, we can write:

(1/3)L = rate × 3

Simplifying this equation, we get:

rate = (1/9)L

Now, according to the problem statement, the marble travels one quarter (1/4) of the length of the path in 3 1/4 seconds. Therefore, we can write:

(1/4)L = rate × (13/4)

Substituting the value of rate from above, we get:

(1/4)L = (1/9)L × (13/4)

Simplifying this equation, we get:

L = 39

Therefore, it takes the marble (1/3) × 3 + (1/4) × (13/4) = 11/4 seconds to travel the full length of the path.

I hope that helps!