# distance word problem

• Jan 31st 2010, 02:46 PM
jjulianmooree1
distance word problem
i can't find out how to solve this. i know the awnser is 325 km, but i don't know how i came to that.

a bus traveling ar 65 km/h takes one and a quarter hours less than a truck traveling at 52 km/h from point a to point b. what is the distance bwtween the 2 citys?(Headbang)
• Jan 31st 2010, 02:51 PM
e^(i*pi)
Quote:

Originally Posted by jjulianmooree1
i can't find out how to solve this. i know the awnser is 325 km, but i don't know how i came to that.

a bus traveling ar 65 km/h takes one and a quarter hours less than a truck traveling at 52 km/h from point a to point b. what is the distance bwtween the 2 citys?(Headbang)

Let the time taken by the truck be t.

$s = v_1t_1 = 65(t-1.25) = 65t - 81.25$

$s = v_2t_2 = 52t$

Rearrange 2nd equation

$t = \frac{s}{52}$

sub in that equation into the first equation to find s
• Jan 31st 2010, 02:53 PM
jjulianmooree1
ya...but
i'm in gr. 9. i can't rally understand ters such as subing in and what not. so, basicially i'm saying run that by me again?
• Jan 31st 2010, 02:54 PM
VonNemo19
Quote:

Originally Posted by jjulianmooree1
i can't find out how to solve this. i know the awnser is 325 km, but i don't know how i came to that.

a bus traveling ar 65 km/h takes one and a quarter hours less than a truck traveling at 52 km/h from point a to point b. what is the distance bwtween the 2 citys?(Headbang)

Let $x$ be the distance between the two cities, then

$x=52t$

$x=65(t-\frac{5}{4})$
• Jan 31st 2010, 02:58 PM
jjulianmooree1
oh, that makes more sense. thank you.
• Jan 31st 2010, 03:04 PM
jjulianmooree1
once i do this, it becomes x= 65t - 81.25. don't i need to know t in order to solve this?(Headbang)
• Jan 31st 2010, 03:05 PM
VonNemo19
Quote:

Originally Posted by jjulianmooree1
once i do this, it becomes x= 65t - 81.25. don't i need to know t in order to solve this?(Headbang)

Since x equals x (the distance is the same), set the two equations equal:

$52t=65(t-\frac{5}{4})$
• Jan 31st 2010, 03:06 PM
e^(i*pi)
Quote:

Originally Posted by jjulianmooree1
once i do this, it becomes x= 65t - 81.25. don't i need to know t in order to solve this?(Headbang)

That's where the second equation comes in. The $x = \frac{52}{t}$ one. In my earlier post I rearranged the second equation to make t the subject to facilitate solving the simultaneous equations
• Jan 31st 2010, 03:07 PM
jjulianmooree1
oooooooh... that makes a smige more sense.
• Jan 31st 2010, 03:14 PM
jjulianmooree1
so...t=-6.25, 325 devided by 6.25= 52...yeah... i kind of see it. isn't there an easyer method to find this? a table perhaps?
• Jan 31st 2010, 04:18 PM
VonNemo19
Quote:

Originally Posted by jjulianmooree1
so...t=-6.25, 325 devided by 6.25= 52...yeah... i kind of see it. isn't there an easyer method to find this? a table perhaps?

What could be easier than solving for t in the above equation?! (Wink)

When you find out, tell the world!!!!

Kidding. Anyway, these problems require practice. That's all.