distance word problem

**jjulianmooree1** · January 31st 2010, 02:46 PM

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?

**e^(i*pi)** · January 31st 2010, 02:51 PM

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?

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

**jjulianmooree1** · January 31st 2010, 02:53 PM

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?

**VonNemo19** · January 31st 2010, 02:54 PM

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?

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

$x=52t$

$x=65(t-\frac{5}{4})$

**jjulianmooree1** · January 31st 2010, 02:58 PM

oh, that makes more sense. thank you.

**jjulianmooree1** · January 31st 2010, 03:04 PM

once i do this, it becomes x= 65t - 81.25. don't i need to know t in order to solve this?

**VonNemo19** · January 31st 2010, 03:05 PM

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?

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

$52t=65(t-\frac{5}{4})$

**e^(i*pi)** · January 31st 2010, 03:06 PM

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?

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

**jjulianmooree1** · January 31st 2010, 03:07 PM

oooooooh... that makes a smige more sense.

**jjulianmooree1** · January 31st 2010, 03:14 PM

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?

**VonNemo19** · January 31st 2010, 04:18 PM

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?!

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

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

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