## calculusxy one year ago In a race, Alice and Brenda started at the same time and ran with constant spends of 12 km and 20 km per hour, respectively. If Alice crossed the finish line 1 minute after Brenda, how many kilometers long was the race?

1. calculusxy

@jim_thompson5910

2. calculusxy

Since it said "minute" somewhere in the problem, I thought of converting the 12km/hr and 20km/hr into minutes. But I am not sure if that's how I am supposed to start it or if that's even correct.

3. calculusxy

$\frac{ 12 }{ 60 } = \frac{ 1km }{ 5minutes }$ $\frac{ 20 }{ 60 } = \frac{ 1 km }{ 3 minute }$

4. ybarrap

A minute is 1/60 hr, right? So $$(t+1/60)12=20t$$ Solve for t then plug back in to find the total distance t is in hours Does this make sense

5. calculusxy

So I I just use your formula then I will get it correct?

6. calculusxy

12t + 1/5 = 20t 12t - 12t + 1/5 = 20t - 12t 1/5 = 8t 1/5 / 8 = 8t / 8 1/40 = t

7. jim_thompson5910

looks good, now plug that into either side of the original equation to find the distance 20t is the easier side

8. calculusxy

20/40 = 1/2 Okay thanks :)

9. calculusxy

But how did @ybarrap make that equation?

10. jim_thompson5910

he used d = r*t d = distance r = rate t = time

11. calculusxy

Also, we are learning about the method called "Backsolving" so if you can help me with that on this problem.

12. jim_thompson5910

on the left side r = 12 t is t+1/60 on the right side r = 20 t is just itself: t

13. jim_thompson5910

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14. jim_thompson5910

|dw:1436397210345:dw|

15. jim_thompson5910

|dw:1436397232035:dw|

16. calculusxy

So since she is a minute slower, we have to add the 1 right?

17. jim_thompson5910

18. jim_thompson5910

time is converted to hours because the speeds are in km/hr

19. calculusxy

Oh I am sorry.

20. jim_thompson5910

thats fine

21. ybarrap

Sorry had to leave @calculusxy, loved your questions to this problem! Thanks @jim_thompson5910 for following-up!