Question

Starting at home, Jessica traveled uphill to the grocery store for 181818 minutes at just 202020 mph. She then traveled back home along the same path downhill at a speed of 606060 mph. What is her average speed for the entire trip from home to the grocery store and back?

Answer 1

Explanation:

let normal speed=x

speed uphill=x-y

speed downhill=x+y

x-y=20

x+y=60

2x=80

x=40

speed uphill=20 mph

time=18 minutes=\frac{18}{60}=\frac{3}{10} hrs

distance=speed ×time=20×\frac{3}{10}=6 miles

downhill speed=60 mph

time taken=\frac{6}{60}=\frac{1}{10} hr

total time =\frac{3}{10}+\frac{1}{10}=\frac{3+1}{10}=\frac{4}{10}

total distance=6+6=12 mile

average speed=12÷\frac{4}{10}=12×\frac{10}{4}=30 mph

total time=

Answer 2

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

Explanation:

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).