# Word Problem Help!

• Mar 23rd 2008, 07:11 PM
dude
Word Problem Help!
Need to come up with Equation and assign variables D=R*T for the following

Two people set out simultaneously from two locations 12 miles apart and walk toward each other. One person walks 5 miles an hour faster than the other. Find the rate of speed of each person if they meet in one hour and ten minutes.

Any help?
• Mar 23rd 2008, 07:31 PM
topsquark
Quote:

Originally Posted by dude
Need to come up with Equation and assign variables D=R*T for the following

Two people set out simultaneously from two locations 12 miles apart and walk toward each other. One person walks 5 miles an hour faster than the other. Find the rate of speed of each person if they meet in one hour and ten minutes.

Any help?

Let person 1 start at the origin and person 2 start at the 12 mile mark and let person 2 walk at a rate of 5 mi/h faster than person 1.

Then for person 1:
$\displaystyle D_1 = D$ which is unknown
$\displaystyle R_1 = R$ (also unknown)
$\displaystyle T_1 = 70 \text{ minutes}$

So
$\displaystyle D = 70R$

Person 2:
$\displaystyle D_2 = 12 - D_1$
$\displaystyle R_2 = R + 5$
$\displaystyle T_2 = 70 \text{ minutes}$

So
$\displaystyle 12 - D = 70(R + 5)$

So solve the set of simultaneous equations
$\displaystyle D = 70R$
$\displaystyle 12 - D = 70(R + 5)$
for D and R.

-Dan
• Mar 23rd 2008, 07:35 PM
Jen
Quote:

Originally Posted by dude
Need to come up with Equation and assign variables D=R*T for the following

Two people set out simultaneously from two locations 12 miles apart and walk toward each other. One person walks 5 miles an hour faster than the other. Find the rate of speed of each person if they meet in one hour and ten minutes.

Any help?

Well, we know the distance=d=12miles, the time=t=7/6 hours
the rate is either x or for the faster person x+5, well than the effective rate is 2x+5
$\displaystyle 12=(2x+5)\cdot(\frac{7}{6})$
Then all you have to do is solve for x for the slower person and the faster person will be that value + 5. :)
Hope that helps.