Question

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 1

Answer:

• Trip to work has rate:  24 mph

• Trip back to home has rate: 18 mph

• Distance to work is:  480 m

Step-by-step explanation:

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

i.e.

$Speed=\dfrac{Distance}{Time}$

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:

$S_1=\dfrac{x}{20}$

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

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

$S_2=\dfrac{x}{30}$

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

This means that:

$S_1-S_2=8$

i.e.

$\dfrac{x}{20}-\dfrac{x}{30}=8\\\\i.e.\\\\\dfrac{30x-20x}{600}=8\\\\i.e.\\\\\dfrac{10x}{600}=8\\\\i.e.\\\\\dfrac{x}{60}=8\\\\i.e.\\\\x=480\ \text{m}$

Hence, the distance to work is:  480 m.

Also, the rate while going to work is:

$=\dfrac{480}{20}\\\\=24\ \text{mph}$

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

$=\dfrac{480}{30}\\\\=16\ \text{mph}$