word problem help...2 varying speeds known, time is known, distance unknown

[slowlearner]

I would appreciated some help with this problem, thank you in advance.

John leaves home drives to the store and turns around and comes right back(assume he forgot his money)

He drove 20km/hour on the way and 25km/hour on the way back. The total return trip took him 9/10 of an hour.

What is the total distance John drove?

 

[JeffM]

I would appreciated some help with this problem, thank you in advance.

John leaves home drives to the store and turns around and comes right back(assume he forgot his money)

He drove 20km/hour on the way and 25km/hour on the way back. The total return trip took him 9/10 of an hour.

What is the total distance John drove?

My way to solve word problems is to start by defining briefly what are the unknowns and assigning a letter to each.

Let O = distance one way.

Let B = distance both ways.

My second step is to translate the conditions of the problem from words into math. We have two unknowns so we need two equations. The first equation is so obvious that most people would do it automatically in their heads.

B = O + O = 2 * O.

So O = distance one way.

And B = distance both ways = 2 * O.

So we need to find an equation involving O. But there is a general formula relating distance, time, and speed. What is it?

How do we use that formula to find O?

 

[Deleted member 4993]

I would appreciated some help with this problem, thank you in advance.

John leaves home drives to the store and turns around and comes right back(assume he forgot his money)

He drove 20km/hour on the way and 25km/hour on the way back. The total return trip took him 9/10 of an hour.

What is the total distance John drove?

Hint:

1) Assume the distance traveled one way is d km

2) Use distance-rate-time equation.

3) derive expression for time-to-drive-up (t_u) and time-to-drive-down (t_d) in terms of d

d) add (t_u) and (t_d) and equate to 9/10 hour - and solve for d. (The word total leads me to beleive that the author is refering to time required for round-trip - poor choice of words)

Please read the post titled "Read before Posting".

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[slowlearnerone]

here is what i got but i do not know if it is right

i have a hard time knowing how to set the question up -
here is what i have;


d=rt

d = (20km/hr + 25km/hr)/2 x 9/10 of an hour

= 22.5km/hr x 9/10 of an hour

= 20.25km which is the total distance round trip




Could this be it?
How do you know when you look at the question if it is a system of equations involving 2 variables or just how i did it above?


Thanks for responding

Hint:

1) Assume the distance traveled one way is d km

2) Use distance-rate-time equation.

3) derive expression for time-to-drive-up (t_u) and time-to-drive-down (t_d) in terms of d

d) add (t_u) and (t_d) and equate to 9/10 hour - and solve for d.


Please read the post titled "Read before Posting".

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[slowlearnerone]

Thank you
Yes the d=rt formula
and you are using 2 variables therefore 2 equations
i dont know a lot of the times from looking at a question whether i should try and set up 2 different equations or just one

With this problem;
one way distance = 20km/hour multiplied by time, but we dont know how long it took one way, we only know the total time for round trip.

is it ok to take the average rate of speed and use that to determine the total distance?

Thanks for responding

My way to solve word problems is to start by defining briefly what are the unknowns and assigning a letter to each.

Let O = distance one way.

Let B = distance both ways.

My second step is to translate the conditions of the problem from words into math. We have two unknowns so we need two equations. The first equation is so obvious that most people would do it automatically in their heads.

B = O + O = 2 * O.

So O = distance one way.

And B = distance both ways = 2 * O.

So we need to find an equation involving O. But there is a general formula relating distance, time, and speed. What is it?

How do we use that formula to find O?

 

[JeffM]

Thank you
Yes the d=rt formula
and you are using 2 variables therefore 2 equations
i dont know a lot of the times from looking at a question whether i should try and set up 2 different equations or just one

With this problem;
one way distance = 20km/hour multiplied by time, but we dont know how long it took one way, we only know the total time for round trip.

is it ok to take the average rate of speed and use that to determine the total distance?

Thanks for responding

OK This is why I like my step by step method. It helps to break the problem down into very small pieces.

What don't we know?

Well we do not know the round-trip distance, but we do know that it is twice the one way distance.

And you are absolutely right that the piece of general knowledge that is not given in the problem but we are expected to know is

\(\displaystyle d = r * t \implies r = \dfrac{d}{t} \implies t = \dfrac{d}{r}.\)

And you are right that we do not know the total time for the round trip, but what do we know? Well, we know both the rate and the time for the return trip. So we can calculate the distance for the return trip. But if we know the distance for the trip one way, it is a cinch to compute the distance both ways.

Can you do the problem now?

Think of math problems as a detective story. In a good detective story, you are given all the clues, but they are hidden. What do we know, and what are we trying to find out: those are always the fundamental problem. If you are still stuck, please ask more questions.