SOLUTION: If Paul drives at 60 mph to work and arrives 1 hour early. But when he drives at 40 mph he arrives 1 hour late. What is the appropriate speed Paul should go at? i know the answe

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Question 320814: If Paul drives at 60 mph to work and arrives 1 hour early. But when he drives at 40 mph he arrives 1 hour late. What is the appropriate speed Paul should go at?
i know the answer is 48mph i just dont get how which is what i need help on
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the basics: Distance equals Rate times Time

Let represent the actual distance to work. Let be the amount of time it would take him to get to work if he arrives on time.

That means that the amount of time required to go distance at 60 miles per hour must be -- that's because he gets there an hour early. And the amount of time to go that same distance at 40 miles per hour must be , one extra hour, meaning one hour late.

So, since we know , we can write:



and we can also write:



But the distance to work doesn't vary just because he travels at a different speed, so since , we can write:



Solve for





So now we know that it should take him 5 hours to get to work IF he drove at a speed that would get him there right on time.

So if he gets there one hour early at 60 miles per hour, then at 60 it takes him 4 hours, 60 times 4 is 240. And now we know the distance to work is 240 miles.



miles per hour.

Now THAT is a killer commute. The guy drives 10 hours a day in order to work for 8 hours a day. Why don't math teachers consider the real world when they concoct word problems?

John

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
If Paul drives at 60 mph to work and arrives 1 hour early. But when he drives at 40 mph he arrives 1 hour late. What is the appropriate speed Paul should go at?
i know the answer is 48mph i just dont get how which is what i need help on

Make this chart

                 DISTANCE    RATE     TIME
When early     
When late         
When on time       

We will assume he always starts out at exactly the same time, whether
he is early, late, or on time.  Let t be the time from when he
always starts out until he is due to be at work.  Let r be the rate
he should drive to get there on time from the time he always starts.

Fill in the rates, 60, 40 and r, ad fill in t for the time when on time.


                 DISTANCE    RATE     TIME
When early                    60     
When late                     40 
When on time                   r       t

When he is 1 hour early, his time is 1 hour less than t, or t-1
When he is 1 hour late, his time is 1 hour more than t, or t+1
Fill those in:

                 DISTANCE    RATE     TIME
When early                    60      t-1
When late                     40      t+1
When on time                   r       t

Now use DISTANCE = RATE × TIME to fill in the three distances.

                 DISTANCE    RATE     TIME
When early        60(t-1)     60      t-1
When late         40(t+1)     40      t+1
When on time        rt         r       t

Now, we realize that all three distances are equal:

Setting the first two distances equal:

60(t-1) = 40(t+1)
 60t-60 = 40t + 40
    20t = 100
      t = 5 hrs.

Wow!  He certainly commutes a long way to work!!!!! He drives longer
than he works!!!!!  But nevertheless, that's the way the problem goes.

Setting the second and third distances equal:

 40(t+1) = rt
 40(5+1) = r(5)    
   40(6) = 5r
     240 = 5r
      48 = r
       r = 48 mph

Checking:

When he is on time, he travels 5 hours at 48 mph, his distance to work is 240 miles. (wow, what a long commute!)

When he is 1 hour early, he travels only 4 hours at 60 miles an hour, and that
also gives us that he commutes 240 miles to work.  So that part checks.

When he is 1 hour late, he travels 6 hours at 40 miles an hour, and that
also gives us that he commutes 240 miles to work.  So that part also checks.

So we know we are right. He drives 5 hours to work, works 8 hours, and drives home 5 hours, and only has 6 hours 
to sleep before he has to get up and drive to work again!  No way he'll live to age 35.

Edwin