Answer:
A biker has 216 miles distance from home to work.
Step-by-step explanation:
Given:
Time required in usual speed = 4 hours.
Let usual speed be x
Hence distance can be calculated by multiplying time with speed we get.
Distance = [tex]Speed \times Time = 4x[/tex]
Also Given;
When the weather is bad, he travels 6 mph slower, and it takes him half an hour more
New speed will be 6 less than usual speed.
Hence Speed = [tex]x-6[/tex]
Also time required will be half an hour more than time required in usual speed.
Time = 4+0.5 = 4.5 hrs
Now distance can be calculated by multiplying time with speed we get.
Distance = [tex]Speed \times Time[/tex]
Substituting the values we get;
[tex]4x=(x-6)4.5\\4x=4.5x-27\\4.5x-4x=27\\0.5x =27\\x = \frac{27}{0.5}=54 mph[/tex]
Hence Speed = 54 mph
Now Distance = [tex]4x=4\times 54 =216 \ miles[/tex]
Hence Distance from home to work is 216 miles.
