Answer:
Brady rides at slower speed which is 17 miles/hours for <em><u>3 hours and 36 minutes.</u></em>
Step-by-step explanation:
Given:
Brady rode 70 miles in 4 hours.
For
hours he rode at the average rate of 17 miles/hour
For rest of the time he rode at the average rate of 22 miles per hour.
To find the time Braady rode at the slower speed.
Solution:
Total time of riding = 4 hours
Time for which Brady rides at 17 miles/ hour =
hours
Distance covered in
hours = ![Speed\times time=17\times t =17t\ miles](https://tex.z-dn.net/?f=Speed%5Ctimes%20time%3D17%5Ctimes%20t%20%3D17t%5C%20miles)
So, time for which Brady rides at 22 miles/ hour =
hours
Distance covered in
hours = ![Speed\times time=22\times(4-t) =(88-22t)\ miles](https://tex.z-dn.net/?f=Speed%5Ctimes%20time%3D22%5Ctimes%284-t%29%20%3D%2888-22t%29%5C%20miles)
Total distance can be given as:
⇒ ![17t+88-22t](https://tex.z-dn.net/?f=17t%2B88-22t)
Simplifying.
⇒ ![-5t+88](https://tex.z-dn.net/?f=-5t%2B88)
Total distance given =70 miles.
Thus, the equation to find
can be given as:
![-5t+88=70](https://tex.z-dn.net/?f=-5t%2B88%3D70)
Subtracting both sides by 88.
![-5t+88-88=70-88](https://tex.z-dn.net/?f=-5t%2B88-88%3D70-88)
![-5t=-18](https://tex.z-dn.net/?f=-5t%3D-18)
Dividing both sides by -5.
![\frac{-5t}{-5}=\frac{-18}{-5}](https://tex.z-dn.net/?f=%5Cfrac%7B-5t%7D%7B-5%7D%3D%5Cfrac%7B-18%7D%7B-5%7D)
∴
hours
![3.6\ hours = 3\ hour+ (0.6\times 60)\ minutes = 3\ hour\ 36\ minutes](https://tex.z-dn.net/?f=3.6%5C%20hours%20%3D%203%5C%20hour%2B%20%280.6%5Ctimes%2060%29%5C%20minutes%20%3D%203%5C%20hour%5C%2036%5C%20minutes)
Thus, Brady rides at slower speed which is 17 miles/hours for 3 hours and 36 minutes.