## safia21 5 years ago Ryan drives 10mi/h slower than Maya, And it takes ryan 1 hour longer to travel 300 miles. How long does it take Maya to make a trip

1. sandra

I'll let amistre get this :p

2. sandra

well, you need two equations and two variables to be able to solve this

3. sandra

one variable is the time it takes Maya to take the trip, and one variable is the time it takes ryan to take the trip

4. safia21

I got 300(x)= 300(x-1) + 10x(x-1)

5. sandra

well, actually, let's make the two variables the speed of each person - then we can easily solve for how long it takes maya to drive 300 miles. So: 1. R = M - 10 2. 300/R - 300/M = 1

6. anonymous

i think i have an answer.

7. sandra

what did you get?

8. anonymous

i got 60 but it was kind of a pain the way i did it. maybe an easier way.

9. anonymous

i used maya's rate as r, ryan's as r - 10 and then $\frac{300}{r}=\frac{300}{r-10}+1$

10. anonymous

that is ryan's time is one hour more than maya's.

11. sandra

right. yeah that makes sense

12. safia21

sorry but i do not understand

13. anonymous

i made a mistake somewhere i am trying again.

14. anonymous

first of all the answer: ryan travels at 50 mpr and maya at 60. it is easy to check: $d=rt$ $t=\frac{d}{r}$ if maya travels 300 miles at 60 miles an hour she makes the trip in $\frac{300}{60}=5$ hours while ryan takes $\frac{300}{50}=6$ hours or one hour longer. so this is the correct answer.

15. safia21

O i understand thank you!

16. anonymous

well i got the correct answer, but i am trying to find the right algebra to solve it for you.

17. anonymous

whew finally. ok here goes. ready?

18. safia21

yes!

19. anonymous

ok we use $t=\frac{d}{r}$ and we know that ryans rate is r-10 and his maya's time is one less than ryan's. Maya's time is $\frac{300}{r}$ and ryan's is $\frac{300}{r-10}$ and $\frac{300}{r}-1=\frac{300}{r-10}$

20. anonymous

that says maya's time is one less than ryans. to solve for r, easiest to subtract first on the left hand side: $\frac{300-r}{r}=\frac{300}{r-10}$ now cross multiply: $(r-10)(300-r)=300r$ mutiply out $300r-3000-r^2+10r=300r$ subtract 300r $-3000 -r^2+10r=0$

21. anonymous

damn

22. anonymous

thought i had $(r-60)(r+50)=0$ so r = 60 but i seem to have made another mistake somewhere. i will try to find it.

23. anonymous

oh lord. i put the one on the wrong side! should have been $\frac{300}{r}+1=\frac{300}{r-10}$

24. anonymous

maya's time plus one gives ryans time. ok now. $\frac{300+r}{r}=\frac{300}{r-10}$ $(300+r)(r-10)=300r$ $300r -3000+r^2-10r=300r$ $r^2-10r-300=0$ $(r-60)(r+50)=0$ $r=60$ or $r=-50$ which makes no sense in this problem so $r=60$ sorry it took a while.

25. safia21

its okay and thanks again

26. anonymous

sorry i made a mistake originally. hope it was not too confusing.

27. safia21

it wasnt thanks