Problema Solution
The surface temperature of a deep, spring –fed lake is 70F. The lake temperature drops 2 degrees F for each yard below the lake surface until a depth of 6 yards is reached. From 6 yards to 15 yards deep the temperature is constant. From 15 yards down to the spring source, the temperature increases 3 degree F per foot until the spring source is reached at 20 yards below the surface.
A) What is the temperature at 10 yards below the surface?
B) What is the temperature at 50 feet below the surface?
C) Write an expression for finding the lake temperature at the spring source.
Answer provided by our tutors
A)
Surface temperature: 70F
6 yards bellow the surface the temperature will drop by 2*6 = 12 F to 70 - 12 = 58F
From 6 yards to 15 yards deep the temperature is constant: 58F
Since 10 yards is in the interval between 6 yards and 15 yards the temperature 10 yards bellow the surface is 58F.
B)
1 yd = 3 ft
50 ft = 15*3 + 5
50 ft = 15 yd 5 ft
From 15 yards down to the spring source, the temperature increases 3 degree F per foot thus 5 ft bellow 15 yd the temperature will increase by 3*5 = 15F and become 58 + 15 = 73F.
C)
The spring source is 20 yd bellow the surface.
The temperature 15 yd bellow the surface is 58F.
The source is another 20 - 15 yd - 5 yd = 5*3 = 15 ft bellow the 15 yd thus the temperature will increase by 3*15 = 45 ft and become: 58 + 45 = 103F.