distance problem

Question

franchesca and julio jog around a circular track that is 500 meters long. Julia's rate is 250 meters per minute, while Ferris's rate is only 230 meters per minute. In how many minutes will Julia be a full lap ahead in terms of minutes?

Answer 1

You may use d = rt and spend lots of time on homework or standardized tests. Or --

The question is: How long does it take Julia to get ONE FULL LAP ahead of Franchesca? Or, worded more simply, how long does it take for Franchesca to run ONE FULL LAP to catch up to Julia if she suddenly stopped?

In all of the solutions, you will se 500/20 = 25. So, why not start there (and save lots of time)?

Answer 2

Here's one way, but there may be a more straightforward solution.

Distance = Rate x Time Julio's distance d_j = 250t_j so t_j = d_j/250

Similarly for Francesca, d_f = 230t_f so t_f = d_f/230

We also know that Julio must be 1 lap ahead after some period of time (assume they started together), that's 500 meters, so d_j = d_f + 500

t_j = t_f so d_j/250 = d_f/230 Substituting: (d_f + 500)/250 = d_f/230

Cross-multiply: 250d_f = 230(d_f + 500) -> 250d_f = 230d_f + 115000 -> 20d_f = 115000, d_f = 5,750 meters.

Then d_j = 5,750 + 500 = 6,250 meters. Now we get to the question of time!

t_j = 6250/250 = 25 minutes; t_f = 5750/230 = 25 min also. Answer is 25 min.for Julio to be a lap ahead.

Answer 3

Hello here is the following solution,

Information we have

1. Ferris and Julia jogged around a circular track = 500 meters long.
2. Julia's rate = 250 meters per minute
3. Ferris's rate = 230 meters per minute.

What we want to find out

1. In how many minutes will Julia be a full lap ahead in terms of minutes?

Steps for Solution

1. Determine what are your variables and create equations.
2. Rate × Time = Distance or r × t = d , where r = rate , t = time & d = distance.
3. Giving us the following
4. Julias rate = 250 meters per minute = 250t = distance = J_D
5. Ferris rate = 230 meters per minute = 230t = distance = F_D
6. To find how many minutes will Julia be a full lap ahead we will create the following equations
7. J_D − F_D = 500 meters
8. 250t - 230t = 500

Solving 250t - 230t = 500

20t = 500

t = 25 minutes

Therefore Julia will be 25 minutes ahead.

Hope that helps!

Answer 4