Math Problem (+rep)

[PTER]

From his home in Point Alexander, Dan drove to Belleville at an average speed of 75 km/h. From her home in Chalk River, Ashley drove through Point Alexander to Bellebille at an average speed of 85 km/h.
The distance from Chalk River to Point Alexander is 18 km. If dan and Ashley left at the same time,
a) after what length of time did Ashley over take Dan?

b) how far were they from Point Alexander when Ashley overtook Dan?


The answers are a) 1.8 h b) 135 km but i need to know how to solve it.. thanks!

[Jamesy]

Divide 18 by the speeds they are going and find the differene. I think, It's still too early in the morning for it to be sure...

[PTER]

Could you solve it fully? i need a solution lol

[Ramones]

right son, let's work it.

First off you need to know

Distance = speed x time
Speed = Distance / time
Time = Distance / speed

It took Ashley 18/85 h (distance divided by speed) to get from Chalk River to Point alexander . This is how long Dan was driving before
Ashley reached his starting point. Lets say T is the time elapsed AFTER Ashely reached PA.

Dan's position on road from Point Alexander to Belleville:
75*(18/85) + 75*T

Ashley's position on road from PA to B: 85*T

For what T is 75*(18/85) + 75*T = 85*T

Now mate, you have the forumla to work out everything. E.g for part a) you want to work out T so,

75*(18/85) + 75*T = 85*T
Minus 75*T from both sides:
75*(18/85) = 10*T
Divide both sides by 10:
T = 75*(18/85)/10.
T= 1.58h
THEN ADD THE TIME IT TOOK ASHLEY TO GET FROM CHALK RIVER TO POINT ALEXANDER SO ADD 18/85.

T= 1.58 + 0.21
T = 1.8 rounded.

THANKYOU

[Jesus-Egg]

This is how I would do it:

Firstly, let's call the time at which they overtake t, and the distance between Point Alexander and the place where they overtake s.

You know that distance = velocity x time

For Dan:
s = 75t

For Ashley:
s + 18 = 85t

So all you need to do is solve the simultaneous equations

sub s = 75t into the second equation:
75t + 18 = 85f
18 = 10t
t = 1.8h

then sub this into the first equation:
s = 75(1.8)
s = 135km

easy