Question

A biker travelling at his usual speed can go from his house to work in 4 hours. When the weather is bad, he travels 6 mph slower, and it takes him half an hour more. How far is his work from his house?

Answer 1

A biker has 216 miles distance from home to work.

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 =
`Speed * Time = 4x`

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 =
`x-6`

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 =
`Speed * Time`

Substituting the values we get;

`4x=(x-6)4.5\\4x=4.5x-27\\4.5x-4x=27\\0.5x =27\\x = (27)/(0.5)=54 mph`

Hence Speed = 54 mph

Now Distance =
`4x=4* 54 =216 \ miles`

Hence Distance from home to work is 216 miles.