Question

The total distance in centimeters a toy robot moves varies directly with the time in seconds. The toy robot moves a total distance of 156 centimeters in 12 seconds.

What is the time in seconds the toy robot moves when the total distance is 312 centimeters?
Question 9 options:

24 s

13 s

17 s

Answer 1

Since the total distance the toy robot moves varies directly with the time, we can use the equation:

\[ d = kt \]

where:
- \( d \) is the distance,
- \( t \) is the time,
- \( k \) is the constant of variation.

From the information given, when \( d = 156 \) cm, \( t = 12 \) s. We can find the constant \( k \):

\[
156 = k \cdot 12
\]

Solving for \( k \):

\[
k = \frac{156}{12} = 13
\]

Now we have the relationship:

\[
d = 13t
\]

Next, we want to find the time \( t \) when the total distance \( d = 312 \) cm.

\[
312 = 13t
\]

Solving for \( t \):

\[
t = \frac{312}{13} = 24
\]

Thus, the time in seconds the toy robot moves when the total distance is 312 centimeters is:

**24 s**