Answer:
Maximum speed of bird A is [tex]192\,\,\frac{mi}{h}[/tex]
Maximum speed of bird B is [tex]32\,\,\frac{mi}{h}[/tex]
Step-by-step explanation:
This is a problem with two unknowns: Max speed of bird A (we name that "A"), and max speed of bird B (we call that "B"). Now we can create two equations with these two unknowns, based on the info provided:
Equation 1): based on the phrase "bird A can travel six times as fast as bird B" we write:
[tex]A=6\,*\, B\\A=6B[/tex]
Equation 2): based on the phrase; "the total speeds for these two birds is 224 miles per hour", we write:
[tex]A+B=224\,\,\frac{mi}{h}[/tex]
Now, we use the first equation to substitute A in the second equation, ad then solve for the unknown B:
[tex]A+B=224\,\,\frac{mi}{h}\\(6B)+B=224\,\,\frac{mi}{h}\\7B=224\,\,\frac{mi}{h}\\B=\frac{224}{7} \,\,\frac{mi}{h}\\B=32\,\,\frac{mi}{h}[/tex]
Now we can solve for the other unknown "A" using the substitution equation and the value of B we just found:
[tex]A=6B\\A=6\,(32\,\,\frac{mi}{h})\\A=192\,\,\frac{mi}{h}[/tex]
