A soda machine takes 3 seconds to fill a 15-ounce cup. If t represents the time in seconds, which equation can you use to find how long it takes the machine to fill a 40-ounce cup?

The equation is y = kt where y is the number of ounces and t is the time. According to the formula time it takes to fill 40ounce cup is 8seconds.

Step-by-step explanation:

If a soda machine takes 3 seconds to fill a 15-ounce cup where t is in seconds, it will take t seconds to fill 40ounce cup.

Let the amount of ounce filled by the machine be directly proportional to the time taken to fill the cup. Taking y as the amount of ounce and t as the time taken.

Mathematically, y = kt where k is the constant of proportionality. To get k, since a soda machine takes 3 seconds to fill a 15-ounce cup, from the information,

y = 15 and t = 3

since k = y/t

k = 15/3 = 5

To get the time taken to fill 40ounce cup, we will use the relationship y = kt where k = 5 and y = 40. Substituting this values in the formula to get t, we have;

40 = 5t

t = 40/5

t = 8seconds

The required equation is y = kt where y is the amount of ounces and t is the time.

Information we know:

a 15 ounce cup takes 3 second to fill

determine variables:

x=3

y=15

rate:

y/x=3/15 = 0.2

fixture an equation:

y=kx

y=0.2x

plug in 40 for x:

y=0.2 (40)

=8

Thus, it should take 8 seconds to fill a 40-ounce cup of soda.