many more miles of road are left to build .
<u>Step-by-step explanation:</u>
Here we have , A construction crew must build 4 miles of road in one week. On Monday, they build 1/2 mile of road. On Tuesday, they build 1/3 mile of road. We need to find that How many more miles of road are left to build . Let's find out:
- On Monday, they build 1/2 mile of road.
- On Tuesday, they build 1/3 mile of road.
Let Miles of road left to build is x So,
⇒ ![\frac{1}{2} +\frac{1}{3} +x = 4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2B%5Cfrac%7B1%7D%7B3%7D%20%2Bx%20%3D%204)
⇒ ![x = 4 - (\frac{1}{2} +\frac{1}{3})](https://tex.z-dn.net/?f=x%20%3D%204%20-%20%28%5Cfrac%7B1%7D%7B2%7D%20%2B%5Cfrac%7B1%7D%7B3%7D%29)
⇒ ![x = 4 - (\frac{1(3)+1(2)}{6} )](https://tex.z-dn.net/?f=x%20%3D%204%20-%20%28%5Cfrac%7B1%283%29%2B1%282%29%7D%7B6%7D%20%29)
⇒ ![x = 4 - (\frac{5}{6} )](https://tex.z-dn.net/?f=x%20%3D%204%20-%20%28%5Cfrac%7B5%7D%7B6%7D%20%29)
⇒ ![x = (\frac{4(6)-5}{6} )](https://tex.z-dn.net/?f=x%20%3D%20%20%28%5Cfrac%7B4%286%29-5%7D%7B6%7D%20%29)
⇒ ![x = \frac{24-5}{6}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B24-5%7D%7B6%7D)
⇒ ![x = \frac{19}{6}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B19%7D%7B6%7D)
Therefore,
many more miles of road are left to build .