Answer:
4 mph
Step-by-step explanation:
The average speed of an object is given by the total distance covered by the time taken:
[tex]v=\frac{d}{t}[/tex]
where
d is the total distance covered
t is the time taken
in the first part, the person runs for 0.4 hours at a speed of 7 mph, so the distance covered in the 1st part is
[tex]d_1 = v_1 t_1 = (7)(0.4)=2.8 mi[/tex]
Then the distance covered in the second part is [tex]d_2[/tex], so the total distance is
[tex]d=2.8+d_2[/tex] (1)
The total time elapsed is 0.4 hours (first part) + 0.8 hours (second part), so
[tex]t=0.4+0.8=1.2 h[/tex]
So we can write the average speed as
[tex]v=\frac{2.8+d_2}{1.2}[/tex] (1)
We want the average speed to be 5 mph,
v = 5 mph
Therefore we can rearrange eq.(1) to find d2:
[tex]d_2 = 1.2v-2.8 = (1.2)(5)-2.8=3.2 mi[/tex]
And therefore, the speed in the second part must be
[tex]v_2=\frac{d_2}{t_2}=\frac{3.2}{0.8}=4 mph[/tex]
