word problem with d=rt

[kgalewine]

Amy drove from Denver to Boulder during rush hour at an average speed of 30mph and drove home at an average speed of 45mph. If the round trip took 1.75 hours, how far is Boulder from Denver?

I know I should use d=rt for the formula, but I just don't understand how to set this problem up. Please help me! Thanks, Grace.

 

[mmm4444bot]

Hello Grace:

When dealing with "distance-rate-time" exercises, try to remember the following.

Distance can be expressed as a product (r*t).

Rate can be expressed as a ratio (d/t).

Time can be expressed as a ratio (d/r).

You can use the time ratio, to set up an equation to solve for d, because they give values for r each way.

d = distance from Denver to Boulder

The time it took Amy to drive from Denver to Boulder is d/30 hours.

The time it took Amy to drive from Boulder to Denver is d/45 hours.

These two times must sum to 1.75 hours, so there's your equation to solve for d.

Please show whatever work that you can, or explain what you're thinking, if you would like more help with this exercise.

Cheers ~ Mark

 

[kgalewine]

1.75=d/30 + d/45 but how do you get anything from there?

I tried solving the problem before I got your post and I did it as d=45*(1/2)(1.75) and got that d = 39.375 miles, which I am guessing is wrong?

 

[Denis]

1.75 = d/30 + d/45 but how do you get anything from there?

That is correct equation: are you saying you cannot solve it for d?

 

[mmm4444bot]

1.75 = d/30 + d/45

but how do you get anything from there ?

Huh ?

Just solve the equation for d.

Once you have the solution for d, you've got the answer to your exercise because the symbol d represents the requested distance.


got that d = 39.375 miles, which I am guessing is wrong ?

There's no need to guess; you can always check any candidate solution by substitution into the original equation.

I mean, if you're wondering whether or not 39.375 miles is the correct answer, do this:

d/30 + d/45 = 1.75

39.375/30 + 39.375/45 = 1.75

1.3125 + 0.875 = 1.75

2.1875 = 1.75

The end result is clearly false.

This easy process confirms that 39.375 miles is not correct because it requires 2.1875 hours of driving time instead of 1.75 hours.

Grace,

If you're trying to tell us that you don't know how to solve linear equations, then it's better to simply say so.

There are different approaches, to solve the equation for d.

Some people like to clear the fractions, first. You can do that by multiplying both sides of the equation by the Least Common Multiple (LCM) of 30 and 45.

Some people like to combine d/30 + d/45 into a single ratio, first, followed by cross-multiplication. Do you know how to use a common denominator, to add two fractions ?

What's your pleasure.

If I misinterpreted your question, please explain it to me.

Cheers ~ Mark

 

[mmm4444bot]

before I got your post and I did it as d=45*(1/2)(1.75)

I just realized what you might have been thinking.

Did you reason that (1/2)(1.75) would be the driving time each direction ?

If so, that's an error in logic because the speeds are unequal.

I mean, if you drive faster, it does not take as much time; if you drive slower, it takes more time.

Alternatively, we realize that the ratios d/30 and d/45 cannot be equal because we're dividing the same numerator by different denominators.

I hope that makes sense.