Two people can complete a task in t hours, where t must satisfy the equation $t25+t30=1\frac { t } { 25 } + \frac { t } { 30 } = 1$ . 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

Two people can complete a task in t hours, where t must satisfy the equation

t25+t30=1\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

Gurdeep Singh · Accepted Answer

Final Answer : B, Explanation :   We can solve for t by finding a common denominator and then simplifying:   t 25 + t 30 = 6 t 150 + 5 t 150 = 11 t 150 = 1 \frac{t}{25} + \frac{t}{30} = \frac{6t}{150} + \frac{5t}{150} = \frac{11t}{150} = 1 25 t ​ + 30 t ​ = 150 6 t ​ + 150 5 t ​ = 150 11 t ​ = 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 t must satisfy the equation $t25+t30=1\frac { t } { 25 } + \frac { t } { 30 } = 1$ . 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

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