A new type of pump can drain a certain pool in 7 hours. An older pump can drain the pool in 13 hours. How long will it take both pumps working together to drain the pool?
Accepted Solution
A:
Answer:Both the pumps together will drain the pool in 4.55 hours.Step-by-step explanation:Pool can be drained by a new pump in the duration = 7 hoursOlder pump can drain the pool in the time = 13 hoursPer hour capacity of the new pump to drain the pool = [tex]\frac{1}{7}[/tex] part of the poolPer hour capacity of the older pump = [tex]\frac{1}{13}[/tex] part of the poolWhen both the pumps work together then part of the pool drained in one hour = [tex]\frac{1}{7}+\frac{1}{13}[/tex]= [tex]\frac{7+13}{91}[/tex]= [tex]\frac{20}{91}[/tex]Since [tex]\frac{20}{91}[/tex] part of the pool is drained in the time = 1 hour, therefore full pool will be drained in the duration = [tex]\frac{1}{\frac{20}{91} }[/tex] = [tex]\frac{91}{20}[/tex]= 4.55 hours