## anonymous one year ago Can someone please explain in the simplest way how to solve this? Michelle rode her bicycle from her house to school at an average speed of 8 miles per hour. Later that daym she rode school back home along the same route at an average speed of 12 miles per hour. If the round trip took her 1 hour, how many miles is the round trip?

1. misty1212

Hi!!

2. misty1212

don't you hate word problems?

3. misty1212

we can do it though for sure

4. anonymous

ok, thanks!

5. misty1212

we are gong to use distance equals rate time time time, or time is distance divide by rate

6. misty1212

we don't know what the distance is, so lets call it D

7. misty1212

time going it $\frac{D}{8}$right?

8. anonymous

yes..

9. misty1212

and time returning is?

10. anonymous

D/12

11. misty1212

right so total time is $\frac{D}{8}+\frac{D}{12}$ which your are told is 1

12. misty1212

solve $\frac{D}{8}+\frac{D}{12}=1$ for $$D$$ and you are done

13. misty1212

do you know how to do that?

14. misty1212

oh btw they ask for the round trip, so once you find D the answer is actually 2D

15. anonymous

Do we need to find a common denominator first?

16. misty1212

you can to that and then add probably be easier to multiply both sides by the least common multiple of 8 and 12 which is 24 that will clear the annoying fractions

17. anonymous

I did it the first way because it was easier for me, I got D = 4.8

18. misty1212

i didn't do it, let me check

19. anonymous

And then 2*4.8 = 9.6. Thank you so much for helping!

20. misty1212

if you multiply by 24 you get $3 d+2 d=24\\ 5D=24\\ D=4.8$ yeah you are righ t

21. misty1212

$\color\magenta\heartsuit$

22. anonymous

that was extremely helpful. thank you again. :)

23. misty1212

you are quite welcome