Answer :
Speed of Joe is 6 mph and that of Beatrice is 8 mph
Step-by-step explanation:
Let Joe's speed be S
Beatrice's speed be s + 2
Let Joe's time be T
Beatrice's time = T - 1/2
Then
We know that
[tex]speed = \frac{distance}{time}[/tex]
Now
Distance =[tex]speed \times time[/tex]
On substituting the value
Equation corresponding to Joe
[tex]12 = S \times T[/tex]...........................(1)
Equation corresponding to Beatrice
[tex](S+2) \times (T - \frac{1}{2})=12[/tex]
Now solving for s and T,we get
[tex](S+2) \times (\frac{12}{S}- \frac{1}{2})=12[/tex]
[tex](S+2) \times (\frac{24 -S}{2S})=12[/tex]
[tex]2S(S+2) \times ({24 -S})=12(2S)[/tex]
[tex](2S^2 - 4S )(24-S) = 24S[/tex]
S = 6 mph -------------------------- Joe's speed
T = 2 hours ------------------------ Joe's time
Thus Beatrice's speed is
6 + 2 = 8 mph
Beatrice's time is
[tex]2 -\frac{1}{2} =1\frac{1}{2 }hours[/tex]