SOLUTION: I am trying to help my daughter with this word problem and I am struggling. Here is the problem: Sherry is travelling from Los Angeles to Miami. On the way there she travels at a

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Question 1089920: I am trying to help my daughter with this word problem and I am struggling. Here is the problem:
Sherry is travelling from Los Angeles to Miami. On the way there she travels at a speed of 40 mph. She stays in Miami for 20 hours then returns home travelling at 35 mph. She is gone from her home a total of 47 hours.

What is the equation using t as the variable to represent the amount of time that Sherry spent driving from Los Angeles to Miami?
What is the distance from Los Angeles to Miami?
Any help you an offer would be great.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52770)   (Show Source): You can put this solution on YOUR website!
.
I am trying to help my daughter with this word problem and I am struggling. Here is the problem:
Sherry is travelling from Los Angeles to Miami. On the way there she travels at a speed of 40 mph.
She stays in Miami for 20 hours then returns home travelling at 35 mph. She is gone from her home a total of 47 hours.

What is the equation using t as the variable to represent the amount of time that Sherry spent driving from Los Angeles to Miami?
What is the distance from Los Angeles to Miami?
~~~~~~~~~~~~~~~~~~~ 

It is clear that the time Sherry spent on the way to there and back is 47 - 20 = 27 hours.


Let D be the distance from the two cities. 


Then the time spent for the travel from LA to Miami is t =  hours.

   By the way, this formula  is what the first question asking for.


Next, the time spent for the travel back is  hours.

The sum is exactly 27 hours:

 +  = 27.


It is the equation to find the distance D.


To solve it, multiply both sides by 35*40. You will get

35D + 40D = 27*35*40,

75D = 27*35*40  ====>  D =  =  504.


Answer.  The distance is 504 miles.

Solved.


Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
I am trying to help my daughter with this word problem and I am struggling. Here is the problem:
Sherry is travelling from Los Angeles to Miami. On the way there she travels at a speed of 40 mph. She stays in Miami for 20 hours then returns home travelling at 35 mph. She is gone from her home a total of 47 hours.

What is the equation using t as the variable to represent the amount of time that Sherry spent driving from Los Angeles to Miami?
What is the distance from Los Angeles to Miami?
Any help you an offer would be great.
Total time spent away from home: 47 hours

Time spent in Miami: 20 hours

Therefore, time spent DRIVING to and fro: 47 - 20, or 27 hours

Time she spent driving from LA to Miami: t

Time she spent driving from Miami to LA = 27 - t



Average speed from LA to Miami: 40 mph

Average speed on return trip:   35 mph

Distance traveled from LA to Miami, at 40 mph: 40t

Distance traveled from Miami to LA, at 35 mph: 35(27 - t)



It's obvious that the distance from LA to Miami, and back is the same.

Thus, the following DISTANCE equation is formed: 

40t = 945 - 35t ------- Distributing the 35 on the right

75t = 945 ------- Adding 35t to both sides 

t, or time spent driving from LA to Miami: 

Distance from LA to Miami:  

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