Two runners, one averaging 5 miles per hour and the other averaging 4 miles per hour, start at the same place and run along the same trail. The slower runner arrives at the end of the trail a quarter of an hour after the faster runner. How far did each person run?

Question

anonymous · Answer

Two given rates, two related times, one equal distance.
You can set up two $distance=rate\times time$ equations and set the distances equal to solve.

anonymous · Answer

I did that. I just was not getting the correct answers when I try to multiply the LCD into each side of the equation.

anonymous · Answer

hmm, ok, .. can you show me the equations you used?

anonymous · Answer

$$20(\frac{ x }{ 5 })+20(\frac{ x }{ 4 })=$$

anonymous · Answer

What's on the other side of the equals sign? Your equation isn't complete. Also, how does  it take into consideration the +0.25 hour of time for the slower runner?

anonymous · Answer

According to the problem the slower running comes in 1 hour after the fast runner. I just figured out the problem but I don't know how I actually came to the final number. I got 5 miles per hour now. Some how I was not completing it somewhere and I was only get 20.

anonymous · Answer

Now I'm not sure if we're reading the same question. I'm seeing

$r_A=5$

$r_B=4$

$d_A=d_B=d$

$t_B=0.25+t_A$

Find d.

$d=r*t$

$(r_A)(t_A)=(r_B)(0.25+t_A)$

Let $t_A=t$

$5t=4(0.25+t)$

Solve for t, plug in to either distance equation to find distance.