Answer:
![1(5)/(7)\text{ days}](https://img.qammunity.org/2019/formulas/mathematics/high-school/gty7infexm1m5rpdjk2xpylmu1lgvq8yjr.png)
Explanation:
Given,
Rollin can wash all the dogs in 4 hours,
The work done by Rollin in one day =
![(1)/(4)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/55daype98oi47j2b5nw9r26vt4buk0otmp.png)
Also, Sam can wash all the dogs in 3 hours,
The work done by Sam in one day =
![(1)/(3)](https://img.qammunity.org/2019/formulas/mathematics/high-school/o3yxzdkdyrjbyds67gthccgpjakv6mdcfp.png)
The total work done by both Rollin and Sam in one day =
![(1)/(4)+(1)/(3)=(3+4)/(12)=(7)/(12)](https://img.qammunity.org/2019/formulas/mathematics/high-school/1qpm0uojuvoxz37jjvn07815j0q1o1pcs4.png)
Hence, the time taken by them when they work together =
![(1)/(7/12)=(12)/(7)=1(5)/(7)\text{ days}](https://img.qammunity.org/2019/formulas/mathematics/high-school/x1hxokaolrg6bzlcyab1wokxo4ikyi38ol.png)