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

$1\ hour=60\ minutes$

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

$20=\frac{x}{(3/10)} \\ \\x=20*\frac{3}{10}\\ \\x=6\ miles$

Step 2

Find the time t2

$60=\frac{6}{t2} \\ \\t2=\frac{6}{60}\\ \\t2=\frac{1}{10}\ hours$

Step 3

Find the average speed for the entire trip

we know that

the average speed is equal

$\frac{2x}{(t1+t2)}=\frac{2*6}{\frac{3}{10}+\frac{1}{10}} \\ \\=\frac{12}{(2/5)}\\ \\=30\ mph$

therefore

the answer is

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