SOLUTION: I have a story problem using d=rt, where is the distance, r is the rate and t is the time. Suppose you are traveling at an average of 55 miles per hour to your sisters house, a

Question 334470: I have a story problem using d=rt, where is the distance, r is the rate and t is the time.
Suppose you are traveling at an average of 55 miles per hour to your sisters house, and return at an average of 65 miles per hour. The total driving time is 12 hours. How far, in miles did you travel?
The only option that even comes close to the answer I get is 660. I can not figure out how.
Please help!! thanks so much!
Found 2 solutions by nerdybill, josmiceli:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Suppose you are traveling at an average of 55 miles per hour to your sisters house, and return at an average of 65 miles per hour. The total driving time is 12 hours. How far, in miles did you travel?
.
Let x = time (hours) it takes to travel to your sister's house
then
12-x = time (hours) it takes to return from your sister's house
.
Distance to your sister's house: d = rt
55x
Distnace from your sister's house:
65(12-x)
.
Since the distance is the same whether you're going to or returning from your sister's house, set both expressions (above) equal to each other and solve for x:
55x = 65(12-x)
55x = 780-65x
120x = 780
x = 6.5 hours (time to travel TO your sister's house)
.
Distance then must be:
55x = 55(6.5) = 357.5 miles

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You can write 2 equations, 1 for driving to the house and
1 for returning. The distance is unknown, but it's the
same for both trips. I'll call the distance
I'll call the time to drive to the house . Since the
total driving time is hrs, the time to drive back
is
Driving to the house:
(1)
Drive from the house:
(2)
given:
mi/hr
mi/hr
-------------------------
Now I can write:
(1)
(2)
I can set (1) and (2) equal to eachother:

It took 6.5 hrs to drive to the house.
Now find

mi
You drove the same distance coming back, so
the total distance is

You drove 715 mi
check answer:

OK
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