Question

The oil in a lamp burns at a linear rate. The lamp contained 13 ounces of oil ten minutes after it was lit. It contained seven ounces of oil 38 minutes after it was lit. What was the original volume of oil before the lamp was lit?

Answer 1

Since the oil in the lamp burns at a linear rate, we can say that it follows an arithmetic progression. For an arithmetic progression, the formula for finding the nth term is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence(initial volume of oil)

n represents the number of terms(the time )

d represents the common difference(The constant amount by which the volume of oil is decreasing)

Tn represents the volume of oil left after n minutes

Looking at the information given, the following equations can be derived

For the first equation,

13 = a + (10 - 1)d

13 = a + 9d

For the second equation,

7 = a + (38 - 1)d

7 = a + 37d

subtracting the second equation from the first equation, it becomes

6d = 28