If you usually burn after 1/2 hour expose to sun, you can lenghten the time you are in the sun to three hours by applying SPF number 6. how long could a person who burns after 1/4 hour stay in the sun using SPF 15 lotion?

To determine how long a person who burns after 1/4 hour can stay in the sun using SPF 15 lotion, we can use the concept of Sun Protection Factor (SPF).

SPF measures how much longer the skin can be exposed to the sun without burning compared to not wearing any sunscreen. It is calculated by dividing the amount of time it takes for the skin to burn without any protection by the amount of time it takes to burn with a particular SPF sunscreen.

In this case, if a person usually burns after 1/2 hour of sun exposure and can lengthen the time to three hours using SPF 6 lotion, we can calculate the effectiveness of the lotion.

Using SPF 6 lotion, the person can stay in the sun 6 times longer than without any protection. So, with SPF 6 lotion, the person can stay in the sun for 1/2 hour x 6 = 3 hours.

Now, let's calculate how long the same person can stay in the sun using SPF 15 lotion.

If the person burns after 1/4 hour of sun exposure, and SPF 15 lotion is 15 times more effective than no sunscreen, we can set up a proportion:

1/2 (burn time without any protection) : 1/4 (burn time with SPF 15) = 6 (SPF 6 effectiveness) : x (unknown SPF 15 effectiveness)

Using cross-multiplication, we get:

(1/2) / (1/4) = 6 / x

Multiplying both sides by (1/4), we have:

1/2 = (6 / x) * (1/4)

Simplifying, we get:

1/2 = 6 / 4x

Now, cross-multiply:

2 * 6 = 4x

12 = 4x

Divide by 4:

x = 12 / 4

x = 3

Therefore, using SPF 15 lotion, the person who burns after 1/4 hour can stay in the sun for up to 3 hours.