WORD PROBLEM

Question

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?

Answer 1

d = uphill distance = downhill distance

 

v = uphill speed = 10 mph

 

t₁ = uphill time = 24 minutes * (1 hour)/(60 minutes) = 0.4 hours

 

d = vt₁ = (10 mph)(0.4 hrs) = 4 miles

 

u = downhill speed = 30 mph

 

t₂ = downhill time = d/u = (4 miles) / (30 mph) = 2/15 hours

 

The time weighted average speed is

 

⟨v⟩ = (t₁v + t₂u) / (t₁ + t₂) = [0.4*10 + (2/15)*(30)] miles / [(0.4 + 2/15) hours]

 

⟨v⟩ = (8 miles) / [(0.4 + 2/15) hours] = 15 miles/hour

 

You get the same result by dividing total distance traveled by total travel time:

 

⟨v⟩ = 2d / (t₁ + t₂) = 2*(4 miles) / [(0.4 + 2/15) hours] = 15 mph