A family is taking a trip. During the first 2 hours, they travel at a rate of 25 miles per hour. They then take a break for 2 hours and do not travel during that time. They finally travel again for another 3 hours at a rate of 40 miles per hour before stopping for the day. What is the average speed for their first day of travel? How much time elapsed from the start of their trip until they stopped for the day? Δt=

Average speed v = 24.29 mph

Total time taken ∆t = 7 hours

Step-by-step explanation:

Given;

the first 2 hours, they travel at a rate of 25 miles per hour

t1 = 2 hours

v1 = 25 mph

then take a break for 2 hours and do not travel during that time

t2 = 2 hours

v2 = 0

They finally travel again for another 3 hours at a rate of 40 miles per hour before stopping for the day.

t3 = 3 hours

v3 = 40 mph

Total time taken ∆t = sum of time taken for the day travel

∆t = t1 + t2 + t3

Substituting the values;

∆t = 2 + 2 + 3 = 7 hours

The average speed v = total distance travelled/total time taken

v = d/∆t ... 1

Total distance travelled d = Σ (velocity * time)

d = v1t1 + v2t2 + v3t3

d = 25 * 2 + 0*2 + 40 * 3

d = 50 + 0 + 120

d = 170 miles

Substituting into equation 1.

v = 170 miles : 7 hours

Average speed v = 24.29 mph