How far to the bottom?

Question

A hiker climbs a mountain path at the rate of 2 miles per hour. Following the same path down the mountain, the joker has a rate of 4 miles per hour. If the round trip took 3 hours, how far is it from the top to the bottom of the mountain?

Answer 1

First we will assign the following:

 

D = distance from top to bottom in miles (also bottom to top)

X = Time to climb up the mountain in hours

Y = Time to climb down the mountain in hours

 

X + Y = 3   (Equation 1)

 

Time * Velocity = Distance

X*2 = D (2 mph is the velocity to climb up the mountain)  --- (Equation 2)

Y*4 = D (4 mph is the velocity to climb down the mountain)  --- (Equation 3)

 

Equation 2 = Equation 3 since Distance is the same going up and down

X*2 = Y*4

X = Y*2

 

Substitute the above into Equation 1

Y*2 + Y = 3

3*Y = 3

Y = 1

 

Time to climb down is 1 Hour

Time to climb up: X + 1 = 3 => X = 2 => 2 Hours

 

Distance = Time * Velocity

D = 2*X = 4 miles