Answer:
F = 7 hours
Step-by-step explanation:
Let the time taken by Frank to work alone be F.
Translating the word problem into an algebraic equation;
Thomas alone takes (F - 4) hours.
Combine time = 2.1 hours
Their individual work rate expressed in piles per hour are;
Frank = 1/F
Thomas = 1/(F - 4)
Combined rate = 1/F + 1/(F - 4)
Simplifying the equation, we have;
Combined rate = (F - 4 + F)/F(F - 4)
Combined rate = (2F - 4)/F(F - 4)
Combined rate = (2F - 4)/(F²- 4F)
Now to find the time taken when they work together is;
(2F - 4)/(F²- 4F) = 1/2.1
Cross-multiplying, we have;
2.1*(2F - 4) = F² - 4F
4.2F - 8.4 = F² - 4F
Rearranging the equation, we have;
F² - 4.2F - 4F + 8.4 = 0
F² - 8.2F + 8.4 = 0
Solving the quadratic equation by factorization;
Factors = -7 and -1.2
F² - 7F - 1.2F + 8.4 = 0
F(F - 7) - 1.2(F - 7) = 0
(F - 7)(F - 1.2) = 0
Therefore, F = 7 or 1.2 hours
The time taken by Frank alone would be 7 hours.
