A cleaning company found that 14 men took 6 h 40 min to clean a large warehouse.?

a)
6 h 80 min = 20/3 h

Fraction of the warehouse cleaned by 1 man in 1 hour
= 1 / [(20/3) × 14]
= 3/280

Time taken for 8 men to clean the warehouse
= 1 / [(3/280) × 8] h
= 35/3 h
= 11 h 40 min


b)
Fraction of the warehouse cleaned by the 8 men in the first hour
= (3/280) × 8 × 1
= 3/35

Fraction of the warehouse cleaned by the remaining 6 men
= 1 - (3/35)
= 32/35

Time taken for the remaining 6 men to clean the warehouse
= (32/35) / [(3/280) × 6] h
= 128/9 h
= 14 h 13 min 20 sec

a)
Time taken for 1 man to clean the warehouse
= (6 h 40 min) × 14
= (400 min) × 14
= 5600 min

Time taken for 8 men to clean the warehouse
= (5600 min) / 8
= 700 min
= 11 h 40 min


b)
Since 1 man takes 5600 min to clean the warehouse,
Then, 1 man clean (1/5600) of the warehouse.

Fraction of the warehouse cleaned by the 8 men in the first hour
= (1/5600) × 8 × 60
= 3/35

Fraction of the warehouse cleaned by the remaining 6 men
= 1 - (3/35)
= 32/35

Time taken for the remaining 6 men to clean the warehouse
= (32/35) / (6/5600 /min)
= (853 and 1/3) min
= 14 h (13 and 1/3) min

you just need to calculate the rate at which 1 man cleans (from the initial statement), then apply it to each subsequent scenario.