Answer:
Average speed of the car A = 70 miles per hour
Average speed of the car B = 60 miles per hour
Explanation:
Average speed of the car A is [tex]v_{A} =\frac{x_{A} }{t_{A} }[/tex] (Equation A) and Average speed of the car B is [tex]v_{B} =\frac{x_{B} }{t_{B} }[/tex] (Equation B), where [tex]x_{A}[/tex] and [tex]x_{B}[/tex] are the distances and [tex]t_{A}[/tex] and [tex]t_{B}[/tex] are the times at which are travelling the cars A and B respectively.
We have to convert the time to the correct units:
1 hour and 36 minutes = 96 minutes
[tex]96 minutes . \frac{1 hour}{60 minutes} = 1.6 h[/tex]
From the diagram (Please see the attachment), we can see that at the time they meet, we have:
[tex]v_{A} = \frac{208-x}{1.6h} + 10\frac{miles}{h}[/tex] (Equation C)
[tex]v_{B} = \frac{208-x}{1.6h}[/tex] (Equation D)
From Equation A and C, we have:
[tex]\frac{208-x}{1.6}+10 = \frac{x}{1.6}[/tex]
208-x+16 = x
208 + 16 = 2x
[tex]x = \frac{224}{2}[/tex]
x = 112 miles
Replacing x in Equation A:
[tex]v_{A} = \frac{112miles}{1.6h}[/tex]
[tex]v_{A} = 70 miles per hour[/tex]
Replacing x in Equation B:
[tex]v_{B} = \frac{208miles-112miles}{1.6h}[/tex]
[tex]v_{B} = \frac{96miles}{1.6h}[/tex]
[tex]v_{B} = 60 miles per hour[/tex]
