Two people can complete a task in t hours, where t must satisfy the equation $$\frac { t } { 25 } + \frac { t } { 30 } = 1$$ . Find the required time t , in hours. Round your answer to two decimal places.
A) $2.20$ hours
B) $13.64$ hours
C) $150.00$ hours
D) $55.00$ hours
E)no solution

Question

Quizplus · Accepted Answer

We can solve for t by finding a common denominator and then simplifying: $$\frac{t}{25} + \frac{t}{30} = \frac{6t}{150} + \frac{5t}{150} = \frac{11t}{150} = 1$$ Multiplying both sides by 150, we get $11t=150$ and $t = \frac{150}{11} \approx \boxed{13.64}$ hours.

Two People Can Complete a Task in T Hours, Where t25+t30=1\frac { t } { 25 } + \frac { t } { 30 } = 125t​+30t​=1

Two People Can Complete a Task in T Hours, Where $\frac { t } { 25 } + \frac { t } { 30 } = 1$