Question 822041
View the rates as kilograms of hay per day.  The rates of the goat and the cow are additive simply.


Goat rate + cow rate = combined rate of goat and cow.
{{{214/60+214/15=C}}}, letting C = their combined rate in kilograms per day.


{{{214/60+(214/15)(4/4)=214/60+856/60=1070/60=107/6}}}, kilograms per day.
This also means, 107 kilograms in 6 days.


How many days, d, for both together to eat 214 kilograms of hay?
{{{(107/6)*d=214}}}
{{{d=214(6/107)=12}}} days.