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 hours
Older pump can drain the pool in the time = 13 hours
Per hour capacity of the new pump to drain the pool = [tex]\frac{1}{7}[/tex] part of the pool
Per hour capacity of the older pump = [tex]\frac{1}{13}[/tex] part of the pool
When 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
