# Word problems (distance)

#### paulmdrdo

##### Active member
1. Professors Roberts and james, who live 676 miles apart,
are exchanging houses and jobs for four months. They
start out for their new locations at exactly the same
time, and they meet after 6.5 hours of driving. If their
average speeds differ by 4 miles per hour, what is each
professor’s average speed?

my work is

let $x=$ prof Robert's speed.
$x+4=$ prof. James' speed.

since the took 6.5 hours to meet each other,

i have

$6.5x+6.5(x+4)=676$

$x=50$

$50$ mph - prof Robert's speed
$54$ mph - prof James' speed.

am I correct?

2. Two cyclists start out at the same time from points
that are 395 kilometers apart and travel toward each
other. The first cyclist travels at an average speed of
40 kilometers per hour, and the second travels at an
average speed of 50 kilometers per hour. After how
many hours will they be 35 kilometers apart?

i don't know where to start here.

Last edited:

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
Re: word problems(distance)

$50$ mph - prof Robert's speed
$54$ mph - prof James' speed.

am I correct?
Yes, except the problem does not say which if the two was going slower.

2. Two cyclists start out at the same time from points
that are 395 kilometers apart and travel toward each
other. The first cyclist travels at an average speed of
40 kilometers per hour, and the second travels at an
average speed of 50 kilometers per hour. After how
many hours will they be 35 kilometers apart?

i don't know where to start here.
How is this harder than problem 1? You know the total distance traveled (395 - 35 = 360km), and you know the speed of each cyclist.

#### mente oscura

##### Well-known member
Re: word problems(distance)

2. Two cyclists start out at the same time from points
that are 395 kilometers apart and travel toward each
other. The first cyclist travels at an average speed of
40 kilometers per hour, and the second travels at an
average speed of 50 kilometers per hour. After how
many hours will they be 35 kilometers apart?

i don't know where to start here.
Hello.

I recommend to you that, always, in this style of questions, you realizes a table. I believe that you will understand it better.

 speed distance time Total $$395-35$$ The firts 40 d t The second 50 $$360-d$$ t

You look, if you can continue.

Regards.

#### paulmdrdo

##### Active member
Re: Word problems(distance)

i don't know if this is correct

my solution.

let $t=$ time it takes for the two cyclists to be 35km apart.

$50t+40t=360$

$90t=360$ then $t=4$

so after 4 hours the two cyclist will be 35 km apart. am I correct?

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
Re: Word problems(distance)

Yes, this is correct.

#### mente oscura

##### Well-known member
Re: Word problems(distance)

Hello.

Yes, it is correct.

Regards.

Edit.

I am sorry, Evgeny. I have seen your respuest later. #### HallsofIvy

##### Well-known member
MHB Math Helper
Re: Word problems(distance)

2. Two cyclists start out at the same time from points
that are 395 kilometers apart and travel toward each
other. The first cyclist travels at an average speed of
40 kilometers per hour, and the second travels at an
average speed of 50 kilometers per hour. After how
many hours will they be 35 kilometers apart?

i don't know where to start here.
They are moving toward each other with a relative speed of 50+ 40= 90 kilometers per hour. Since they were initially 395 kilometers apart, when they are 35 kilometers apart, they must have covered 395- 35= 360 kilometers. It will take 4 hours to cover 360 kilometers at 90 kilometers per hour.