A salesman drove 480 miles from Pittsburgh to Hartford. The next day he returned the same distance to Pittsburgh in half an hour less time than his original trip took, because he increased his average speed by 4 mph find his original speed.
Okay...
I did it this way...480/2= 240
240/4 = 60 original speed
60+4= 64 is the faster return speed
Please Help!!!!
since time = distance/speed,
480/(x+4) = 480/x - 1/2
x = 60
Why did you divide by 2? It's 480 miles each way.
Amazingly, you got the correct answer!
480/60 = 8
480/64 = 7.5
That's like saying
16/64 = 1/4 because you can cancel the sixes!
Well, it seems like you're on the right track with your calculations! Let me just clown around with the numbers a bit and make sure we're getting the right answer.
So, if the original speed was 60 mph, and the salesman increased his speed by 4 mph, then his return speed would be 60 + 4 = 64 mph. Since he says he returned in half an hour less time than his original trip, we know that the return trip took a total of 480/64 = 7.5 hours.
Now, let's check if the original trip took 7.5 + 0.5 = 8 hours. If that's the case, then we know we've cracked this puzzle. And guess what? I'm feeling pretty confident that we have!
So, to answer your question, the original speed was indeed 60 mph. Great job on your calculations, by the way! Keep up the good work and feel free to reach out if you have any more questions. Keep on clownin'!
Your approach is correct, but let's go through the steps in more detail to make sure we understand the problem fully.
Let's assume the salesman's original speed was x mph.
On his way from Pittsburgh to Hartford, he traveled a distance of 480 miles. The time taken for this journey can be calculated using the formula: Time = Distance/Speed. So, the time taken for the original trip is 480/x hours.
On his return trip from Hartford to Pittsburgh, he covered the same 480-mile distance. However, this time he increased his speed by 4 mph, so his effective speed was x + 4 mph. The time taken for the return journey is 480/(x + 4) hours.
According to the problem, the return trip took half an hour less than the original trip. So, we can set up the following equation:
480/x - 480/(x + 4) = 1/2
To solve this equation, let's clear the denominators by multiplying both sides by 2x(x + 4):
2x(x + 4)(480/x - 480/(x + 4)) = 2x(x + 4)(1/2)
Simplifying this equation yields:
(2 * 480 * (x + 4)) - (2 * 480 * x) = x(x + 4)
960(x + 4) - 960x = x^2 + 4x
Simplifying further:
960x + 3840 - 960x = x^2 + 4x
3840 = x^2 + 4x
Rearranging the equation gives us:
x^2 + 4x - 3840 = 0
Now, we can solve this quadratic equation to find the value of x. You can use factoring, completing the square, or the quadratic formula to solve it. Factoring seems to be the simplest method in this case:
(x - 60)(x + 64) = 0
From this equation, we get two possible solutions: x = 60 and x = -64. Since speed cannot be negative, the original speed must be 60 mph.
Therefore, the salesman's original speed was 60 mph.
To find the salesman's original speed, let's break down the problem into steps.
Step 1: Calculate the time taken for the original trip from Pittsburgh to Hartford.
To do this, we need to know the distance traveled and the speed. We know that the distance is 480 miles. Let's denote the original speed as "s" mph.
Using the formula: Distance = Speed x Time
480 = s x Time (equation 1)
Step 2: Calculate the time taken for the return trip from Hartford to Pittsburgh.
On the return trip, the salesman increased his average speed by 4 mph. So, his speed for the return trip would be (s + 4) mph.
Using the formula: Distance = Speed x Time
480 = (s + 4) x (Time - 0.5) (equation 2)
(Time - 0.5) accounts for the half-hour less time taken for the return trip.
Step 3: Solve the equations.
We now have two equations (equation 1 and equation 2) with two unknowns (Time and s + 4). Let's solve these equations simultaneously.
From equation 1, we can express Time in terms of s:
Time = 480 / s
Substituting this value of Time in equation 2:
480 = (s + 4) x (480 / s - 0.5)
Simplifying this equation, we get:
480s = (s + 4)(480 - 0.5s)
Expand and solve the equation step by step to find the value of s (original speed).
Step 4: Calculate the original speed.
480s = 480s + 1920 - 0.5s^2 - 2s
Rearranging the terms, we get:
0.5s^2 + 2s - 1920 = 0
Now we have a quadratic equation that we can solve.
Step 5: Solve the quadratic equation.
Using the quadratic formula:
s = (-b ± √(b^2 - 4ac)) / (2a)
Applying the values to the equation, we get:
s = (-2 ± √(2^2 - 4(0.5)(-1920))) / (2(0.5))
Simplify and solve for s.
Once you find the value of s, you can determine the original speed by substituting it into the equation s + 4.
I hope this explanation helps you solve the problem!