Velocity, distance and time:
This question is solved using the following formula:
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
In which v is the velocity, d is the distance, and t is the time.
On the first day of travel, a driver was going at a speed of 40 mph.
Time
, distance of
, v = 40. So
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
![40 = \frac{d_1}{t_1}](https://tex.z-dn.net/?f=40%20%3D%20%5Cfrac%7Bd_1%7D%7Bt_1%7D)
The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles
On the second day, the velocity is
.
On the first day, he drove 2 more hours, which means that for the second day, the time is: ![t_1 - 2](https://tex.z-dn.net/?f=t_1%20-%202)
On the first day, he traveled 20 more miles, which means that for the second day, the distance is: ![d_1 - 20](https://tex.z-dn.net/?f=d_1%20-%2020)
Thus
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
![60 = \frac{d_1 - 20}{t_1 - 2}](https://tex.z-dn.net/?f=60%20%3D%20%5Cfrac%7Bd_1%20-%2020%7D%7Bt_1%20-%202%7D)
System of equations:
Now, from the two equations, a system of equations can be built. So
![40 = \frac{d_1}{t_1}](https://tex.z-dn.net/?f=40%20%3D%20%5Cfrac%7Bd_1%7D%7Bt_1%7D)
![60 = \frac{d_1 - 20}{t_1 - 2}](https://tex.z-dn.net/?f=60%20%3D%20%5Cfrac%7Bd_1%20-%2020%7D%7Bt_1%20-%202%7D)
Find the total distance traveled in the two days:
We solve the system of equation for
, which gets the distance on the first day. The distance on the second day is
, and the total distance is:
![T = d_1 + d_2 = d_1 + d_1 - 20 = 2d_1 - 20](https://tex.z-dn.net/?f=T%20%3D%20d_1%20%2B%20d_2%20%3D%20d_1%20%2B%20d_1%20-%2020%20%3D%202d_1%20-%2020)
From the first equation:
![d_1 = 40t_1](https://tex.z-dn.net/?f=d_1%20%3D%2040t_1)
![t_1 = \frac{d_1}{40}](https://tex.z-dn.net/?f=t_1%20%3D%20%5Cfrac%7Bd_1%7D%7B40%7D)
Replacing in the second equation:
![60 = \frac{d_1 - 20}{t_1 - 2}](https://tex.z-dn.net/?f=60%20%3D%20%5Cfrac%7Bd_1%20-%2020%7D%7Bt_1%20-%202%7D)
![d_1 - 20 = 60t_1 - 120](https://tex.z-dn.net/?f=d_1%20-%2020%20%3D%2060t_1%20-%20120)
![d_1 - 20 = 60\frac{d_1}{40} - 120](https://tex.z-dn.net/?f=d_1%20-%2020%20%3D%2060%5Cfrac%7Bd_1%7D%7B40%7D%20-%20120)
![d_1 = \frac{3d_1}{2} - 100](https://tex.z-dn.net/?f=d_1%20%3D%20%5Cfrac%7B3d_1%7D%7B2%7D%20-%20100)
![d_1 - \frac{3d_1}{2} = -100](https://tex.z-dn.net/?f=d_1%20-%20%5Cfrac%7B3d_1%7D%7B2%7D%20%3D%20-100)
![-\frac{d_1}{2} = -100](https://tex.z-dn.net/?f=-%5Cfrac%7Bd_1%7D%7B2%7D%20%3D%20-100)
![\frac{d_1}{2} = 100](https://tex.z-dn.net/?f=%5Cfrac%7Bd_1%7D%7B2%7D%20%3D%20100)
![d_1 = 200](https://tex.z-dn.net/?f=d_1%20%3D%20200)
Thus, the total distance is:
![T = 2d_1 - 20 = 2(200) - 20 = 400 - 20 = 380](https://tex.z-dn.net/?f=T%20%3D%202d_1%20-%2020%20%3D%202%28200%29%20-%2020%20%3D%20400%20-%2020%20%3D%20380)
The total distance traveled in two days was of 380 miles.
For the relation between velocity, distance and time, you can take a look here: brainly.com/question/14307500