Answer:
Time taken by Doreen is 6 hours and speed is 10 miles per hour.
Time taken by Sue is 4 hours and speed is 20 miles per hour.
Step-by-step explanation:
Let the speed of Doreen be x
According to the question speed of Sue is = x+10
time taken By Sue to cover 80 miles = ![\frac{80}{x+10}](https://tex.z-dn.net/?f=%5Cfrac%7B80%7D%7Bx%2B10%7D)
time taken by Doreen to travel 60 miles = ![\frac{60}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B60%7D%7Bx%7D)
According to question Sue take two hours less than Doreen takes
therefore
-
=2
=2
60(x+10) -80x = 2(x(x+10)
60x+600-80x = ![2x^2+20x\\](https://tex.z-dn.net/?f=2x%5E2%2B20x%5C%5C)
simplifying it ,we get
![2x^2+40x-600=0\\](https://tex.z-dn.net/?f=2x%5E2%2B40x-600%3D0%5C%5C)
Dividing both sides by 2 ,we get
![x^2+20x-300=0\\](https://tex.z-dn.net/?f=x%5E2%2B20x-300%3D0%5C%5C)
solving it for x ,we get
(x+30)(x-10) =0
x =-30 which is not possible
x =10 miles per hour
Speed of Doreen = 10 miles per hour
Speed of Sue = 10+10 = 20 miles per hour
Time taken by Doreen = 60 divided by 10 = 6 hours
Time taken by Sue = 80 divided by 20 = 4 hours