Question

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

Answer 1

trick is to write
\[(\frac{1}{7}+\frac{1}{4})t=1\] and solve for t

Answer 2

Jack:
Time = 7 hrs/job ; rate = 1/7 job/hr

Marilyn:
Marilyn = 4 hrs/job ; rate = 1/4 job/hr

Together DATA:
Time = x hrs/job ; rate = 1/x job/hr

EQUATION:
rate + rate = together rate
1/7 + 1/4 = 1/x
11/28 = 1/x
x = 28/11 = 2.5 hrs

Answer 3

multiply both sides by 28 to get
\[4t+7t=28\]
\[11t=28\]
\[t=\frac{28}{11}\]

Answer 4

@chirs
\[\frac{28}{11}=2\tfrac{6}{11}\] not
\[2.5\] although it is certainly close