# Math Help - another D=rt word problem

1. ## another D=rt word problem

have done a lot of these D=rt problems but this one illuded me.
sure its something so obvious that I did not see it

Sally and Bob live quite far from each other and decide to see each other on Saturday. However, they misunderstand each other and start out at sunrise to go to each others house. At noon they pass each other on the freeway. At 4 pm Sally arrives at Bob's house and at 9 pm Bob arrives at Sally's house. At what time did the sun rise?

First, the distance for both is same and the time between sunrise and noon is the same however unknown. so letting $t$ be the time between sunrise and
noon i set up this equation

$(t+9)R_1 =(t+4)R_2$

in the rates have to be diffent but there has to be a constant ratio between them. In that the answer to this is 6am that shows a ratio of

$\frac{2}{3}R_1=R_2$

so the equation to solve for t is

$(t+9)\frac{2}{3}R_1 = (t+4)R_1$

$2(t+9)=3(t+4)$

$2t + 18 = 3t +12$

$6=t$

however, I don't see how this ratio could be drived from the $9$ and $4$arrival times or how it could be derived if arrival times were different. thanks ahead

2. ## Re: another D=rt word problem

You have not used the fact that "they passed each other at noon". Let X be the distance between there houses. Then you have the three equations:
$X= (t+ 9)R_1$
$X= (t+ 4)R_2$
$tR_1+ tR_2= X$
or just $(t+9)R_1= (t+ 4)R_2= t(R_1+ R_2)$

3. ## Re: another D=rt word problem

Originally Posted by HallsofIvy
or just $(t+9)R_1= (t+ 4)R_2= t(R_1+ R_2)$
i tried solving for t with this and still cannot see how you isolate t with out knowing the ratio between $R_1$ and $R_2$ is