looking for some help

Question

This is a rate-time-distance problem, and I'm confused...

Rebecca rides up a slope on a ski lift at the rate of 120 feet per minute.  She skis from the top to the bottom on a path parallel to the life at a an average rate of 2640 per minute.  How long is the lift if the round trip traveling time is 20-minutes.

Answer 1

Hi Scott, the key to this problem is to remember the distance traveled up on the ski lift is the same as the distance skied down the slope. Let x represent the time it takes to ride the ski lift to the top of the slope, then 20 - x is the time it takes to ski back to the bottom of the slope.

 

Rate-time-distance equation for riding the ski lift to the top of the slope:

 

d_us = x * 120

 

Rate-time-distance equation skiing back to the bottom of the slope:

 

d_ds = (20 - x) * 2640

 

Remember, the distance up the slope is the same as the distance down the slope, then:

 

d_{us =} d_ds

 

Substituting for d_us and d_ds gives:

 

x * 120 = (20 - x) * 2640

 

120x = 52800 - 2640x

 

Adding 2640 to both sides of the equation gives:

 

2640x + 120x = 52800

 

 

Combine like terms:

 

2760x = 52800

 

Divide both sides by 2760 gives:

 

x = 19.13, or the ski lift takes 19.13 minutes to travel from the bottom of the ski lift to the top of the slope.

 

It takes less than a minute to ski from the top of the slope back to the bottom again.

 

Questions?