# Algebra distance word problems

#### bergausstein

##### Active member
A jogger running at the rate of 4 miles per hour takes 45 minutes more than a car traveling at 40 miles per hour to cover a certain course. How long does it take the jogger to
complete the course and what is the length of the course?

i tried to solve this using this method

i let
$x=$ joggers time to complete the course

$x-\frac{3}{4}=$ car time to complete the course

then,

$4x=40\left(x-\frac{3}{4}\right)$

$x=\frac{5}{6}$ or $50$ minutes.

now when i used another method

i let

$x=$time for car to complete the course

$x+\frac{3}{4}=$ jogger's time to complete the course

$40x=4\left(x+\frac{3}{4}\right)$

i get a different answer $x=$12

can you tell me what's the difference between the two solutions i used and which one is correct?

thanks!

Last edited:

#### mente oscura

##### Well-known member
Re: algebra distance word problems

Hello.

You observes.

i tried to solve this using this method

i let
$x=$ joggers time to complete the course

$x-\frac{3}{4}=$ car time to complete the course
Well.

But, then, you apply badly his resolution:

then,

$4x=40\left(x+\frac{3}{4}\right)$

$x=\frac{5}{6}$ or $50$ minutes.
You calculate:

$$x-\dfrac{3}{4}$$

And, then you use, in the resolution:

$$x+\dfrac{3}{4}$$

Regards.

#### bergausstein

##### Active member
Re: algebra distance word problems

yes, but that's just a typo. which I edited now.

my question is, what's the difference in my two solutions and which one is correct?

did I set them up correctly?
in my first solution i chose $x$ to represent the jogger's time so I have $x-\frac{3}{4}=$ for the car's time.

in my second solution i chose $x$ to represent car's time taken to complete the course. so i can have $x+\frac{3}{4}$ to represent jogger's time.

the first solution give $x$ to be $50$mins or $\frac{5}{6}$ of an hour. but the second one give me $x$ to be $12$ which i'm not sure what unit of time should i attached.

please somebody help. this is confusing me.

#### MarkFL

Staff member
Re: algebra distance word problems

In your second method, you obtained an incorrect value for $x$. solving it correctly will give you the same value for the jogger's time.

#### mente oscura

##### Well-known member
Re: algebra distance word problems

$x=$time for car to complete the course

$x+\frac{3}{4}=$ jogger's time to complete the course

$40x=4\left(x+\frac{3}{4}\right)$

i get a different answer $x=$12

Solution:

$$x=\dfrac{1}{12} \ h \ = 5 \ minutes$$

Regards.

#### bergausstein

##### Active member
Re: algebra distance word problems

MARKFL yes, i also noticed that.

but if review my set up in second solution it seems(for me) that's it is correct.

the time taken for the jogger to complete the course is 45mins more than that of the car to complete the same course.

now if i let $x=$ car's time taken to complete the course

then the time taken for jogger should be $x+\frac{3}{4}$

since the travel the same distance i set them equal to one each other.

by $D=RT$

$40x=4(x+\frac{3}{4})$ what's wrong here?

#### mente oscura

##### Well-known member
Re: algebra distance word problems

In your second method, you obtained an incorrect value for $x$. solving it correctly will give you the same value for the jogger's time.
Excuse me, MarkFL.

#### mente oscura

##### Well-known member
Re: algebra distance word problems

$40x=4(x+\frac{3}{4})$ what's wrong here?
This is correct, but you have realized badly the calculations.

Regards.