Riding a bike a person takes 20 minutes to go to work. the trip back home takes 30 minutes. if the rate back is 8 mph slower than the trip to work, find the rates (speeds) each way and the distance to work.

We know that speed is defined as the ratio of distance to time.

i.e.

Let the distance traveled to work be: x m.

Now, while going to work it takes a person 20 minutes.

This means that the speed of the person while going to work is:

Also, the time taken to come back home is: 30 minutes.

This means that the speed of person while riding to home is:

Also, it is given that  the rate back is 8 mph slower than the trip to work.

This means that:

i.e.

Hence, the distance to work is:  480 m.

Also, the rate while going to work is:

and the trip back to home is covered with the speed:

3x + 18 = 147°

step-by-step explanation:

3x + 18 = 147°, because the value of the central angle is equal to the value of the arc formed by it.

i hope i you.