Answer:
The average speed is 30 mph.
Step-by-step explanation:
The rate of change of distance with time is speed.
i.e Speed = [tex]\frac{distance}{time}[/tex]
Let his average speed be represented by s.
Given that she covers 300 miles with an average speed.
So that;
s = [tex]\frac{300}{t}[/tex]
⇒ t = [tex]\frac{300}{s}[/tex] .................. 1
Also, if her average speed has been 7 mph less, she could have traveled only 230 miles in the same length of time. This implies that;
(s - 7) = [tex]\frac{230}{t}[/tex]
⇒ t = [tex]\frac{230}{(s-7)}[/tex] ............... 2
Thus equating 1 and 2, we have;
[tex]\frac{300}{s}[/tex] = [tex]\frac{230}{(s-7)}[/tex]
230s = 300s - 2100
collecting like terms,
2100 = 300s - 230s
2100 = 70s
divide both sides by 70,
s = [tex]\frac{2100}{70}[/tex]
= 30 mph
The average speed is 30 mph.
