Question

A small metal bar whose temperature is 30 C is dropped into a container of 75 C
water. After 1 second the temperature of the bar has increased 1-C. (a) How long
will it take for the temperature of the bar to reach 70-C? (b) 74-C?

Answer 1

It would take about 40 seconds for the temperature to reach 70°C and 44 second to reach 74°C.

Linear equation

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the temperature of the metal bar after x seconds, hence:

Since the metal bar has an initial temperature of 30°C, hence:

b = 30, also m = 1°C (increase), The equation becomes:

y = 1(x) + 30 = x + 30

To reach 70°C:

70 = x + 30

x = 40 seconds

To reach 74°C:

74 = x + 30

x = 44 seconds

It would take about 40 seconds for the temperature to reach 70°C and 44 second to reach 74°C.

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