Question

A certain solar collector can absorb 9.0 MJ in 7.0 h. Another panel is added, and together they collect 41 MJ in 5.0 h. How long would it take the new panel alone to collect 41 MJ?

Answer 1

Lets call the rate at which the first panel absorbs solar energy x:
x = 9/7

To find out how much energy the panel will absorb in a certain number of hours, just multiply x by the time:
In 7 hours, energy = (9/7) * 7 = 9MJ
In 8 hours, energy = (9/7) * 8 = (72/7)MJ

Let's call the rate at which the second panel absorbs solar energy y. Therefore, we can write an equation, in x and y, using the information in the question:
5x + 5y = 41

We know what x is, so 5x = 5 * (9/7) = (45/7):
(45/7) + 5y = 41
5y = 41 - (45/7)

41 is the same as (41*7)/7 = 287/7:
5y = 287/7 - 45/7 = (287-45)/7 = 242/7

Divide both sides by 5 to find the value of y (in MJ absorbed per hours, MJ/h):
y = 242/35 = 6.914285714MJ/h

Let's call the time taken for the new panel to absorb 41MJ t:
ty = 41

We know what y is, so substitute that in and solve:
6.914285714t = 41
t = 41/6.914285714 ≈ 5.929752066 hours

I would like to express this value in the SI unit, which is seconds, s:
5.929752066 * 3600 = 21347.1s