Starting at home, michael traveled uphill to the gift store for 24 minutes at just 10 mph. he then traveled back home along the same path downhill at a speed of 30 mph. what is his average speed for the entire trip from home to the gift store and back?

Average Speed = 15miles per hour

Step-by-step explanation:

This is a velocity-time problem;

Let d = the distance between his home and the uphill

Let v = speed to uphill = 10m/h

Let t = time spent on uphill = 24 minutes convert to hour

t = 24/60 = 0.4 hour

Let u = downhill speed = 30m/h

First, we need to calculate distance, d

Speed = distance/time

Distance = speed * time

Distance, d = 10 * 0.4

Distance = 4m

Then we calculate time spend downhill

Time, t2 = distance/speed

t2 = d/u

t2 = 4/30h

Calculating Average Speed

Average Speed = Distance/Time

Here distance = distance between his house and uphill and distance between uphill and his house

Distance = d + d

Distance = 2d where d = 4m

Distance = 2 * 4m = 8m

Time = total time spent

Time = 0.4 + 4/30

Time = (12+4)/30

Time = 16/30 h

Average Speed = 8/(16/30)

Average Speed = 8 * 30/16

Average Speed = 30/2

Average Speed = 15m/h

His average speed for the entire trip from home to the gift store and back is 15miles per hour