Maths Problem: Help this Shepherd solve his grass problem

A shepherd found that his cow & goat would eat all the grass in a certain field in 45 days, that his cow & donkey would eat it in 60 days, but that it would take his goat & donkey 90 days to eat it all.

If he puts the cow, the goat, and the donkey into the field together, how long will it take them to eat all the grass? Assume that the grass in not growing each day.

Could you please explain and show the steps to solve this problem. Much appreciated.

Thanks
.

Let c = the fraction of a field that the cow can eat in a day; correspondingly g and d for the goat and donkey

so c + g = 1/45
c + d = 1/60
g + d = 1/90

Adding all three equations:
2c + 2g + 2d = 1/20
c + g + d = 1/40

ie. the three animals together eat 1/40 of the field in a day
so they eat the whole field in 40 days