Question 147045: Hi. I am writing is to inform you that I really need help in solving distance word problems. I also will ask you a specific question connected with age word problem. This has nothing to do with home work but I am planning on taking the graduate management admission test (GMAT) probably before the end of this year.
Here are the distance word problems, age word problem and questions connected to these problems:
Problem 1: A 555 mile, 5 hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?
Note: Do not worry about solving the word problem above. Just provide me with the response to the question below.
Here is the part of the equation that I have the question for you:
555-d=115(5-t).
Question 1: I want to know from the above equation, where does this minus "-" sign (555 "-"d=115(5-t) come from? I did read the above distance word problem and I did not see any key words connected with subtration (-). So I need to know where does the (-) come from?
Problem 2: A car and a bus set out at 2pm from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours the car is 20 miles ahead of the bus. Find the rate of the car.
Note: Do not worry about solving the word problem above. Just provide me with the response to the question below.
Here is part of the equation concerning problem 2.
d+20=2(2r-30).
Question 2: I want to know from the above equation, where does this plus "+" sign (d"+"20=2(2r-30) come from? I did read the above distance word problem and I did not see any key words connected with addition (+). So I need to know where does the (+) come from?
Age Word Problem
I noticed this equation with the solution from an age word problem:
H/2+1+H/3-1=20
H/2+H/3=20
3H+2H=120
5H=120
H=24
Question 3: I want to know from the above equation with the solution where does the 120 come from?
Here is the last question:
I solved this equation and I need to know if it is correct:
2r + 20 = 4r - 60
4r - 60
2r + 20
________
2r - 40
-- -- r = -20
2r 2r
The answer is -20. Am I correct?
Thank You.
Note: The above word problems come from a source other than a textbook. It is from a website (www.purplemath.com)
Found 2 solutions by 24HoursTutor.com, MathTherapy:
Answer by 24HoursTutor.com(40)   (Show Source):
You can put this solution on YOUR website! Problem 1
The simple formula below will help us solve the question :
distance = speed X time
The first average speed is = 105km/hr
Let us assume the duration the plane traveled at this speed to be x
The second average speed is =115km/hr
Let us assume the duration the plane traveled at this speed to be y
Now since we know that the total time taken was 5 hrs then the following must be also true :
x + y = 5
From this we can get :
y = 5 -x
Problem 2
Let us assume the speed of the bus to be x
The speed of the car is then = 2x - 30
Distance traveled = speed X time
So, distance traveled by car in 2 hours = 2(2x-30)
And distance traveled by bus = 2 X x = 2x
Now the distance traveled by car is 20 miles more so it means if we add 20 to the distance traveled by bus which is 2x then the distance traveled should be the same. So we can say :
2x+20 = 2(2x-30)
2x+20=4x-60
2x-4x=-60-20
-2x=-80
2x=80
x=80/2
x=40
x is the speed of the bus so now we can say that the speed of the bus is 40km/hr.
Speed of car = 2x-30
=2(40)-30
=80-30
=50
Answer: The average speed of the car is 50km/hr.
Now, distance traveled is 555 km and there are two different speeds at which the plane traveled.
The distance covered by traveling at 105km.hr = speed X time = 105x
The distance covered by traveling at 115km.hr = speed X time = 115y
Total Distance = 105x + 115 y
Now since we are already given the distance we get the following :
555 = 105x+115y
We have previously found out that y=5-x, so we can substitute it in the above equation to get :
555 = 105x + 115(5-x)
555 = 105x + 115x5 - 115x
555 = 105x - 115x + 575
555 = -10x + 575
555-575 = -10 x
-20 = -10x
10x = 20
x=20/10
x=2
Now y = 5-x =5-2 = 3
Ans.: The plane traveled at the speed of 105 km/hr for 2 hours(the value of x) and at the speed of 115km/hr for 3 hours(the value of y)
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Answer by MathTherapy(10719)  (Show Source):
You can put this solution on YOUR website!
Hi. I am writing is to inform you that I really need help in solving distance word problems. I also will ask you a specific question connected with age word problem. This has nothing to do with home work but I am planning on taking the graduate management admission test (GMAT) probably before the end of this year.
===
Here are the distance word problems, age word problem and questions connected to these problems:
=====
Problem 1: A 555 mile, 5 hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?
====
Note: Do not worry about solving the word problem above. Just provide me with the response to the question below.
======
Here is the part of the equation that I have the question for you:
=====
555-d=115(5-t).
====
Question 1: I want to know from the above equation, where does this minus "-" sign (555 "-"d=115(5-t) come from? I did read the above distance word problem and I did not see any key words connected with subtration (-). So I need to know where does the (-) come from?
Problem 2: A car and a bus set out at 2pm from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours the car is 20 miles ahead of the bus. Find the rate of the car.
Note: Do not worry about solving the word problem above. Just provide me with the response to the question below.
Here is part of the equation concerning problem 2.
d+20=2(2r-30).
Question 2: I want to know from the above equation, where does this plus "+" sign (d"+"20=2(2r-30) come from? I did read the above distance word problem and I did not see any key words connected with addition (+). So I need to know where does the (+) come from?
Age Word Problem
I noticed this equation with the solution from an age word problem:
H/2+1+H/3-1=20
H/2+H/3=20
3H+2H=120
5H=120
H=24
Question 3: I want to know from the above equation with the solution where does the 120 come from?
Here is the last question:
I solved this equation and I need to know if it is correct:
2r + 20 = 4r - 60
4r - 60
2r + 20
________
2r - 40
-- -- r = -20
2r 2r
The answer is -20. Am I correct?
Thank You.
Note: The above word problems come from a source other than a textbook. It is from a website (www.purplemath.com)
===================================
===================================
Problem 1: A 555 mile, 5 hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the
tailwind picked up and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?
Note: Do not worry about solving the word problem above. Just provide me with the response to the question below.
Here is the part of the equation that I have the question for you:
555-d=115(5-t).
Question 1: I want to know from the above equation, where does this minus "-" sign (555 "-"d=115(5-t) come from? I did read the above
distance word problem and I did not see any key words connected with subtration (-). So I need to know where does the (-) come from?
The total distance was 555 miles, and there were 2 LEGS during the trip: the 1st leg when the plane traveled at
105 mph, and the 2nd leg when it traveled at 115 mph. Neither the 1st leg's nor the 2nd leg's distance is known.
What is known is the total distance covered over the 2 legs (555 miles). So, the distance covered over the 1st leg
was named "d." Then, obviously, the 2nd leg's (115 mph-LEG) distance was "555 - d" (the total distance, less the
distance covered on the 1st leg).
Hope you understand this!!
========================
Problem 2: A car and a bus set out at 2pm from the same point, headed in the same direction. The average speed of the car is 30 mph slower
than twice the speed of the bus. In two hours the car is 20 miles ahead of the bus. Find the rate of the car.
Note: Do not worry about solving the word problem above. Just provide me with the response to the question below.
Here is part of the equation concerning problem 2.
d+20=2(2r-30).
Question 2: I want to know from the above equation, where does this plus "+" sign (d"+"20=2(2r-30) come from? I did read the above distance
word problem and I did not see any key words connected with addition (+). So I need to know where does the (+) come from?
The ACTUAL distances covered by the car and bus aren't known, so the distance covered by the bus, 2 hours after both
headed out, was named "d."
Two hours after both headed out, the bus had covered "d" miles, while the car, which was 20 miles ahead of the bus, at
that time, had covered "d + 20" miles
Hope you understand this!!
========================================
Age Word Problem
I noticed this equation with the solution from an age word problem:
H/2+1+H/3-1=20
H/2+H/3=20
3H+2H=120
5H=120
H=24
Question 3: I want to know from the above equation with the solution where does the 120 come from?
Multiplying by LCD (Lowest Common Denominator), 6, we get:
Hope you understand this!!
==================
Here is the last question:
I solved this equation and I need to know if it is correct:
2r + 20 = 4r - 60
4r - 60
2r + 20
________
2r - 40
-- -- r = -20
2r 2r
The answer is -20. Am I correct?
No!!! That's WRONG, unfortunately!
2r + 20 = 4r - 60
4r - 60
2r + 20
________
2r - 40 <======= This is WRONG!!
2r - 80 = 0 <=== This is what it should be!!
2r = 80
-- -- r = 40< ==== This is what it should be!!
Hope you understand this!!
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