Final answer:
The correct answer for the time it takes both pumps working together to fill one tank is (a) t = 35/12. This is found by adding the individual rates of the pumps (1/5 and 1/7 tanks per hour, respectively) and taking the reciprocal of the sum (12/35) giving t = 35/12 hours.
Step-by-step explanation:
To find the equation for the time it will take for both pumps working together to fill 1 tank, we need to consider the rate at which each pump can fill the tank individually. The new pump can fill the tank in 5 hours, which means its rate is ⅓ (or 1/5) of a tank per hour. The old pump can fill the tank in 7 hours, which means its rate is ⅔ (or 1/7) of a tank per hour. Working together, you add their rates to find the combined rate:
Rate of new pump + Rate of old pump = Combined rate
⅓ + ⅔ = ⅓+⅔
Combining the fractions gives us:
⅓ x 7 + ⅔ x 5 = 7/35 + 5/35
⅓ = 35/35
Thus, the time, t, for both pumps working together to fill one tank is the reciprocal of the combined rate:
t = 1 / Combined rate
t = 1 / (⅓)
t = 35/12
Therefore, answer (a) t = 35/12 is correct.