a woman drives her car 240 miles in 5 hours. at this rate, how far will she tavel in 8 hours

Question

a woman drives her car 240 miles in 5 hours. at this rate, how far will she tavel in 8 hours

Answer 1

Hi Julia,

 

A good way to approach this problem is to first find the woman's average rate. Think miles per hour when you are driving.  When you're going long distances on the highway, you are usually going around the speed limit, sometimes a little under and sometimes a little over (drive carefully).  Average rate is kind of the speed that you are usually going.  You can also think of it as if you had cruise control on and you had to go the same speed the whole time you were driving.

 

Now, the units are key here: 240 miles per 5 hours in a word problem translates to (240 miles)/(5 hours). This looks like a fraction and with fractions you can divide the numerator (top) by the denominator (bottom).  240/5 will simplify to just a single value and the units will stay the same (miles/hours) because they can't be combined.

 

 

(240 miles)/(5 hours) = (240/5) (miles/hours) = 48 (miles/hours)

 

So the woman was driving for 5 hours and could have been going a little less than 48 miles/hour at some times, a little more at others, but if she ended up driving 240 miles in 5 hours, she had to be traveling at an average rate of 48 miles/hours.

 

The last step is to find the total distance she will travel in the full 8 hours.  Even if you have an equation that uses rate, time and distance, a good way to look at this and fully understand it is again, units.  We have our average rate units (miles/hours) and our total time unit (hours).  If we again recognize that our rate units is miles divided by hours, what would we have to do algebraically to that to change it to just miles? (the question asks for how far she will go)

 

miles/hours(?)hours = miles

 

(miles divided by hours) (+, -, * or /)(hours) = miles.

 

Just like if you add 5 then subtract 5 you get the same value, if you multiply by 5 then divide by 5 you get the same value, too. Or you can even do that in the opposite order since, multiplication and division are on the same order of operations.

 

We can think of units in the same way.  If we divide something by a unit then multiply by the same unit, they will cancel (just like something in the numerator of a fraction cancels the same thing in the denominator).

 

From this, it looks like we need to multiply our rate by our time to have hours cancel hours and be left with just miles.  So we take our rate (48 miles/hours) and multiply by our total time (8 hours).

 

(48 miles/hours)*(8 hours) = 48*8 miles/hours*hours = 384 miles (the total distance she will travel if she continues at her current rate for 8 hours.

 

 

 

I hope that my explanation addresses anything that you might not have fully understood about the problem.  Word problems are tricky to translate and rate and units are always a little confusing in the beginning, but you'll get it.  If you have any further questions you can feel free to respond.

 

Best regards,

 

Josh

 

 

Answer 2

d=rt

 

Set up a proportion

 

240 miles     in 5 hours

x     miles        8 hours

 

5x=1920

 

x=384

At this rate, she can travel 384 miles.

 

OR

 

You could first find her rate in mph (miles per hour)

 

240 miles/5 hours = 48 mph

d=rt

d = 48(8)

d = 348 miles

 

Answer 3

We need to find a rate the rate we are looking for is mph. This is a rate we are familiar with

 

R=240/5 mph = 48 mph

 

Use this rate to determine the distance traveled in 8 hours. 

 

d=Rt

d=48 miles • 8 hours / hours

d=384 miles 

 

Its important to keep the units. When they cancel the units your looking for should remain. The hours cancel leaving miles an appropriate unit for distance.