Answer:
Hence Distance traveled at speed 115 mph is <u>345 miles</u> and Distance traveled at speed 105 mph is <u>210 miles</u>.
Step-by-step explanation:
Given:
Total Distance = 555 mile
Total time = 5 hour
Let time taken to travel at 115 mph be t
So Time taken to travel at 105 mph will be equal to difference between Total time and time taken to travel at 115 mph.
Time taken to travel at 105 mph = ![5-t](https://tex.z-dn.net/?f=5-t)
Distance traveled in speed 105 mph will be equal to speed multiplied by time taken to travel at 105 mph.
Framing in equation form we get;
Distance traveled in 115 mph = ![115t](https://tex.z-dn.net/?f=115t)
Also;
Distance traveled in speed 105 mph will be equal to speed multiplied by time taken to travel at 105 mph.
Framing in equation form we get;
Distance traveled in 105 mph = ![105(t-5) = 105t - 525](https://tex.z-dn.net/?f=105%28t-5%29%20%3D%20105t%20-%20525)
Now Total Distance traveled is equal sum of Distance traveled in 115 mph and Distance traveled in speed 105 mph
![115t-(105t-525)=555\\\\115t-105t+525=555\\\\10t+525=555\\\\10t=555-525\\\\10t=30\\\\t=\frac{30}{10}=3](https://tex.z-dn.net/?f=115t-%28105t-525%29%3D555%5C%5C%5C%5C115t-105t%2B525%3D555%5C%5C%5C%5C10t%2B525%3D555%5C%5C%5C%5C10t%3D555-525%5C%5C%5C%5C10t%3D30%5C%5C%5C%5Ct%3D%5Cfrac%7B30%7D%7B10%7D%3D3)
Time taken to travel at 115 mph = 3 hrs.
Time taken to travel at 105 mph = ![5-t=5-3=2\ hrs](https://tex.z-dn.net/?f=5-t%3D5-3%3D2%5C%20hrs)
Now Distance traveled in 115 mph = ![115t = 115 \times 3 = 345\ miles](https://tex.z-dn.net/?f=115t%20%3D%20115%20%5Ctimes%203%20%3D%20345%5C%20miles)
Distance traveled in 105 mph = ![105(5-t) = 105(5-3)= 105\times 2 = 210\ miles](https://tex.z-dn.net/?f=105%285-t%29%20%3D%20105%285-3%29%3D%20105%5Ctimes%202%20%3D%20210%5C%20miles)
Hence Distance traveled at speed 115 mph is <u>345 miles</u> and Distance traveled at speed 105 mph is <u>210 miles</u>.