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

The average speed is 40 miles per hour.

Answer 2

Based on the formula $distance = velocity*time$ we can find the distance from the grocery store:

$distance = velocity * time = 20mph * \frac{18}{60}hrs = 6 miles$

Based on this distance we can find the time it took her to get back using the formula $time = \frac{distance}{velocity}:$

$time = \frac{distance}{velocity} = \frac{6 miles}{60mph} = \frac{1}{10}hrs = 6 minutes$

After this you just take the average of Jessica going at 20 mph for 18 minutes and 60 mph for 6 minutes:

$\frac{20mph * 18min + 60mph*6min}{24min} = 30mph$

:)