Question 1176759: I need to know the two variables and the 2 equation for this problem.
Your aunt and uncle have been visiting your home. Five
minutes after they drive away, you realize that they forgot
their luggage. You happen to know that they drive at 25
miles per hour. So you get in your car and drive at 30 miles
per hour. How far before you meet
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
for the aunt and the uncle:
their rate is 25 miles per hour.
the formula for them becomes:
25 * time = distance.
for you:
your rate is 30 miles per hour.
the formula for you becomes:
30 * time = distance.
since we already know your rate and their rate, then the only other two variables in the problem that we don't know would be the time and the distance.
the two equations that need to be solved are:
25 * time = distance
30 * time = distance
since the time that they traveled is 5 minutes less than the time that they traveled because they traveled 5 minutes before you started, then we can change the equations to be:
25 * time = distance
30 * (time - 5/60) = distance
since the speeds are in miles per hour, then the time needs to be in hours.
5 minutes divided by 60 is equal to 5/60 hours.
since you had to travel 5 minutes less than them, then you had to travel 5/60 hours less than them.
5 minutes is equivalent to 5/60 hours.
we could have simplified at this point, but it 's not necessary to solve the problem.
since the distance is the same, we can replace the distance with its equivalent in one of the equations to get:
25 * time = 30 * (time - 5/60)
simplify to get:
25 * time = 30 * time - 150/60.
subtract 25 * time from both sides of the equation and add 150/60 to both sides of the equation to get:
150/60 = 30 * time - 25 * time
simplify to get:
150/60 = 5 * time
solve for time to get:
time = (150/60)/5 = 150/300 = 1/2 of an hour.
he caught up to them in 1/2 of an hour.
go back to the original equations to see if that makes sense and to solve for the distance.
the two original equations are:
25 * time = distance
30 * (time - 5/60) = distance
when time = 1/2, these equatons become:
25 * 1/2 = distance = 12.5 miles.
30 * (1/2 - 5/60) = distance = 30 * (30/60 - 5/60) = 30 * 25/60 = 25/2 = 12.5 miles.
the distance is the same at 12.5 miles.
you caught up with them 12.5 miles from the house.
they were traveling for half an hour which is equal to 30 minutes.
you were traveling for 25/60 of an hour which is equal to 25 minutes.
since they left 5 minutes ahead of you, you were traveling 5 minutes less than them when you caught up with them.
it all checks out.
the distance was 12.5 miles from the house when you caught up with them.
that's your answer.
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