Question

If you run for 0.4 hours at 7 mph, how fast should you walk during the next 0.8 hours to have the average speed of 5 mph?

Answer 1

Answer:

4 mph

Step-by-step explanation:

The average speed of an object is given by the total distance covered by the time taken:

$v=\frac{d}{t}$

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

$d_1 = v_1 t_1 = (7)(0.4)=2.8 mi$

Then the distance covered in the second part is $d_2$, so the total distance is

$d=2.8+d_2$ (1)

The total time elapsed is 0.4 hours (first part) + 0.8 hours (second part), so

$t=0.4+0.8=1.2 h$

So we can write the average speed as

$v=\frac{2.8+d_2}{1.2}$ (1)

We want the average speed to be 5 mph,

v = 5 mph

Therefore we can rearrange eq.(1) to find d2:

$d_2 = 1.2v-2.8 = (1.2)(5)-2.8=3.2 mi$

And therefore, the speed in the second part must be

$v_2=\frac{d_2}{t_2}=\frac{3.2}{0.8}=4 mph$