Jack usually mows his lawn in 4 hours. Marilyn can mow the same yard in 7 hours. How much time would it tak for them to mow the lawn together?

Question

Jack usually mows his lawn in 4 hours.  Marilyn can mow the same yard in 7 hours.  How much time would it tak for them to mow the lawn together?

anonymous · Answer

Is the answer 3.23 hours

ybarrap · Answer

j = Jack mows 1 yard in 4 hours = 1/4 yards per hour
m = Marilyn mows 1 yard in 7 hours = 1/6 yards per hour

t = time for both to mow 1 yard
So,
(1/4) t + (1/7) t = 1 yard ,                        
t(1/4 + 1/7) = 1
t = 1/(1/4 + 1/7)
  = 1/11/28
  = 28/11
  = 2.54 hours

Note. In 2.54 hours, jack cuts 2.54 * (1/4) = 0.635 of a yard
         while Marilyn cuts 2.54 * (1/7) = 0.363 of a yard.
         Together in 2.54 hours, they cut .635 + .363 = 1 yard.

Ans. 2.54 hours