. How far can a man walk along the road at four miles an hour and ride back at twenty miles an hour if the entire trip takes six hours?

Answer 1

For this question we will use the formula DISTANCE = RATE * TIME

We know the entire trip takes 6 hours, but we don't know how long each section of the trip takes. Let's call the time that he walks for "X", and the time that he drives for "Y". 

So we know that X + Y = 6 

Walking Section of the Trip

Distance = (4 miles per hour) * X 

Distance = 4X

Driving Section of the Trip

Distance = (20 miles per hour) * Y 

Distance = 20Y 

X+Y = 6, we can rewrite this as Y = 6-X and plug it back into the formula. 

Distance = 20(6-X)

Distance = 120-20X 

We don't know the total distance yet, but we know that for a round trip the trip there will be the same distance as the trip back. So we can combine these equations: 

4X = 120 - 20X 

24X = 120

X = 5 

We can plug this back into either equation for the walking section or driving section. Let's use the Walking section since it's simpler. 

Distance = 4X 

Distance = 4*5 

Distance = 20

Based on the wording of the question, you would answer that he walked 20 miles and rode back 20 miles (the total distance he traveled would be 40 miles).

Answer 2

d = 4t

d = 20(6 - t)

4t = 120 - 20t

24t = 120

t = 5

20 miles