word prob: Find length of trail, given times and rates

[lewysangel]

Two skiers begin skiing along a trail at the same time. The faster skier averages 9 miles per hour and the slower skier averages 6 miles per hour. The faster skier completes the trail 1/4 hour before the slower skier. How long is the trail?

 

[Denis]

t = time by faster skier
9t = 6(t + 1/4) ; solve for t, then use formula speed = distance / time

 

[soroban]

Re: word problem

Hello, lewysangel!

Use: \(\displaystyle \:\text{Distance} \:=\:\text{Speed}\,\times\,\text{Time}\;\;\Rightarrow\;\;\text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}\)

Two skiers begin skiing along a trail at the same time.
The faster skier averages 9 mph and the slower skier averages 6 mph.
The faster skier completes the trail ¼ hour before the slower skier.
How long is the trail?

Let \(\displaystyle d\) = length of the trail (in miles).

The faster skier goes \(\displaystyle d\) miles at 9 mph.
. . His time is: \(\displaystyle \:\frac{d}{9}\) hours.

The slower skier goes \(\displaystyle d\) miles at 6 mph.
. . His time is: \(\displaystyle \:\frac{d}{6}\) hours.

The faster skier's time is ¼ hour less than the slower skier's time.
. . The equation is: \(\displaystyle \L\:\frac{d}{9} \:=\:\frac{d}{6}\,-\,\frac{1}{4}\)

Now solve for \(\displaystyle d.\)