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.

Answer:Trip to work has rate:  24 mphTrip back to home has rate: 18 mphDistance to work is:  480 mStep-by-step explanation:We know that speed is defined as the ratio of distance to time.i.e.[tex]Speed=\dfrac{Distance}{Time}[/tex]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:[tex]S_1=\dfrac{x}{20}[/tex]Also, the time taken to come back home is: 30 minutes.This means that the speed of person while riding to home is:[tex]S_2=\dfrac{x}{30}[/tex]Also, it is given that  the rate back is 8 mph slower than the trip to work.This means that:[tex]S_1-S_2=8[/tex]i.e.[tex]\dfrac{x}{20}-\dfrac{x}{30}=8\\\\i.e.\\\\\dfrac{30x-20x}{600}=8\\\\i.e.\\\\\dfrac{10x}{600}=8\\\\i.e.\\\\\dfrac{x}{60}=8\\\\i.e.\\\\x=480\ \text{m}[/tex]Hence, the distance to work is:  480 m.Also, the rate while going to work is:[tex]=\dfrac{480}{20}\\\\=24\ \text{mph}[/tex]and the trip back to home is covered with the speed:[tex]=\dfrac{480}{30}\\\\=16\ \text{mph}[/tex]