Respuesta :
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 = [tex]\frac{80}{x+10}[/tex]
time taken by Doreen to travel 60 miles = [tex]\frac{60}{x}[/tex]
According to question Sue take two hours less than Doreen takes
therefore
[tex]\frac{60}{x}[/tex] - [tex]\frac{80}{x+10}[/tex] =2
[tex]\frac{60(x+10)-80x}{x(x+10)}[/tex] =2
60(x+10) -80x = 2(x(x+10)
60x+600-80x = [tex]2x^2+20x\\[/tex]
simplifying it ,we get
[tex]2x^2+40x-600=0\\[/tex]
Dividing both sides by 2 ,we get
[tex]x^2+20x-300=0\\[/tex]
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
