Common Type of Problem involving Rtn'l Eqns: Melanie drove 404 km from Point A to...

[markl77]

I don't know if I'm allowed to post twice in a day; but I really need help with this.
This is the question given :

Melanie drove 404 km from Point A to Point B in the same time that it took Heidi to drive 364 km from Point C to Point D. Melanie drove 10km/h faster than Heidi. Determine Heidi's speed in km/h.
(I used Points A,B,C,D instead of real locations.)

I tried to organize the information given in a d=rt graph:


Melanie D: 404 R: (x+10) T: 404/(x+10)
Heidi D: 364 R: (x-10) T: 364/(x-10)

From here I have pretty much no idea what to do... I tried by making them equal because I assumed that the times were both equal so maybe that would give me what x was, but it didn't.

 

[Deleted member 4993]

I don't know if I'm allowed to post twice in a day; but I really need help with this.
This is the question given :

Melanie drove 404 km from Point A to Point B in the same time that it took Heidi to drive 364 km from Point C to Point D. Melanie drove 10km/h faster than Heidi. Determine Heidi's speed in km/h.
(I used Points A,B,C,D instead of real locations.)

I tried to organize the information given in a d=rt graph:


Melanie D: 404 R: (x+10) T: 404/(x+10)
Heidi D: 364 R: (x-10) T: 364/(x-10)

From here I have pretty much no idea what to do... I tried by making them equal because I assumed that the times were both equal so maybe that would give me what x was, but it didn't.

Start over:

Assume Heidi's speed = H

Assume Melanie's speed = M = H +10


Then

404/(H+10) = 364/H

404 * H = 364 * H + 3640

Continue...

Don't forget to check your answer!

 

[markl77]

Start over:

Assume Heidi's speed = H

Assume Melanie's speed = M = H +10


Then

404/(H+10) = 364/H

404 * H = 364 * H + 3640

Continue...

Don't forget to check your answer!

Is there any way you could go more in depth with what this actually means? I got the answer to be 91 km/h for Heidi's speed, but when I try to solve for other questions I still don't know how to organize them in order to find the answer.
What I'm wondering with this is why did you divide Melanie's speed by Heidi's speed + 10 ? I understand that Melanie's speed and Heidi's speed + 10 are equal, so why do you divide those values?

 

[stapel]

[W]hy did you divide Melanie's speed by Heidi's speed + 10 ?

Where are you seeing this division?

To learn how to set up and solve these types of exercises, try here. Then use the set-up method suggested there. To expand upon the previous reply, and using the same variables and the fact that d = rt, so t = d/r, we have:

. . .Heidi:
. . . . .distance: 364
. . . . .rate: H
. . . . .time:364/H

. . .Melanie:
. . . . .distance: 404
. . . . .rate: H + 10
. . . . .time: 404/(H + 10)

You are given that the times are equal, so what should be set equal to create an equation to solve?