Question

Starting at home, Jessica traveled uphill to the grocery store for 18 minutes at just 20 mph. She then traveled back home along the same path downhill at a speed of 60 mph.

What is her average speed for the entire trip from home to the grocery store and back?

Answer 1

Use distance = rate x time

18 minutes is 3/10 of an hour.

So the distance to the store is:
d = 20*(3/10) = 6 miles

The distance downhill is the same, 6 miles. So:
6 = (60)t
6/60 = t
1/10 = t
Where t is the time it took to go back home. So t is .1 hour (6 minutes).

To calculate average speed we use the formula:

average speed = total distance/ total time
average speed = (6+6)/(.3 + .1) = 12/(.4) = 30

So her average speed for the entire trip is 30 mph (miles per hour).

Answer 2

we know that

The speed is equal to the distance divided by the time

Let

x---------> the distance Jessica's home to the grocery store

t1-------> the time from Jessica's home to the grocery store

t2------> the time from grocery store to back home

Step 1

Find the distance x

we have

`t1=18\ minutes`

convert to hour

`1\ hour=60\ minutes`

`t1=18\ minutes=18/60=(3/10)\ hours`

`20=(x)/((3/10)) \\ \\x=20*(3)/(10)\\ \\x=6\ miles`

Step 2

Find the time t2

`60=(6)/(t2) \\ \\t2=(6)/(60)\\ \\t2=(1)/(10)\ hours`

Step 3

Find the average speed for the entire trip

we know that

the average speed is equal

`(2x)/((t1+t2))=(2*6)/((3)/(10)+(1)/(10)) \\ \\=(12)/((2/5))\\ \\=30\ mph`

therefore

the answer is

the average speed for the entire trip is
`30\ mph`