# Rates question (1 Viewer)

#### smithjohn

##### New Member
one route from melbourne to sydney is 950 km. car A leaves melbourne travelling at 90 km/h and car B leaves sydney travelling on the same route at 100 km/h. where will the cars pass each other?

#### CM_Tutor

##### Moderator
Moderator
If A leaves Melbourne travelling to Sydney at 90 km/h then, after $\bg_white t$ hours, A will have travelled $\bg_white 90t$ km along the route.

If B leaves Sydney at the same time as A leaves Melbourne, and B is travelling to Melbourne at 100 km/h along the same route as A is travelling to Sydney, then, after $\bg_white t$ hours, B will have travelled $\bg_white 100t$ km along the route.

Since A and B are travelling along the same route and left their respective starting points at the same time, they will meet when their collective distance travelled equals 950 km, the length of the route. That is:

\bg_white \begin{align*} 90t + 100t &= 950 \\ 190t &= 950 \\ t &= \frac{950}{190} \\ t &= 5 \text{ hours} \end{align*}

So, A and B meet after each travelling for 5 hours. At this time, A has travelled $\bg_white 100 \times 5 = 500 \text{ km}$ and B has travelled $\bg_white 90 \times 5 = 450 \text{ km}$.

So, A and B meet at the point on the route that is 500 km from Sydney a d 450 km from Melbourne.