# Finding distance

#### bkan21

##### New member
Raoul drove at a speed of 50 km/h from Ancaster to Oakville. From Oakville to Sudbury, he drove 80 km/h. If the whole trip was 550km and took 8h, what is the distance from oakville to sudbury

#### Jameson

Staff member
Raoul drove at a speed of 50 km/h from Ancaster to Oakville. From Oakville to Sudbury, he drove 80 km/h. If the whole trip was 550km and took 8h, what is the distance from oakville to sudbury
Hi bkan21,

Welcome to MHB!

You have two variables and two equations. Let x be the time it takes to drive from Ancaster to Oakville and let y be the time it takes to drive from Oakville to Sudbury. From that we can write two relationships using the rest of the information.

$50x+80y=550$ (this is using the fact that $\mbox{rate} \times \mbox{time=distance}$)
$x+y=8$

Can you solve it now? How did you try to solve the problem?

Jameson

#### brosnan123

##### Banned

let x be time from Ancaster to Oakville
let y be the time from Oakville to Sudbury

A->O Distance: 50 x
Speed: 50
Time: x

O->S Distance: 80y
Speed: 80
Time: y

x+y=8 ...............(1)
50x + 80y = 550.........(2)
-50x - 50y = -400.........(3)

30 y = 150............adding (1) and (3)
________________

y= 5

therefore the distance from Oakville to Sudbury =80y = 80 (5)= 400 km