Answer :
Answer:
Gabriella's average original speed was 56 [tex]\frac{mi}{h}[/tex]
Step-by-step explanation:
Let's use the equation that defines the average speed "v" of Gabriella during the time (t) that her trip took:
[tex]v = \frac{distance}{time} \\v=\frac{400}{t}[/tex]
Next let's write a similar average speed equation for the case in which she drove at (v - 7 mi/h) during the same time "t" and covered 350 miles:
[tex](v-7)=\frac{350}{t}[/tex]
Notice that the time "t" in the denominator appears equally in both equations we wrote, so let's isolate them on the right:
[tex]\frac{v}{400} =\frac{1}{t} \\and\\\frac{(v-7)}{350} =\frac{1}{t}[/tex]
now equal both expression since they both share the same value on the right, and solve for the unknown "v":
[tex]\frac{v}{400} =\frac{(v-7)}{350} \\350\,v=400\,(v-7)=\\350\,v=400\,v-2800\\2800=50\,v\\v=\frac{2800}{50} \,\,\frac{mi}{h}\\v=56\,\,\frac{mi}{h}[/tex]