On the first part of a trip to Carmel traveling on the freeway, Marge averaged 70 mph. On the rest of the trip, which was 25 mi longer than the first part, she averaged 60mph. Find the total distance to Carmel if the second part of the trip took 30 minutes more than the first part.
its 95 mi.
Well, it seems like Marge was in quite a hurry to get to Carmel, and then she realized she forgot something and took her time on the second part of the trip! Classic Marge.
Let's break down the problem step by step. First, we know that Marge averaged 70 mph on the first part of the trip, so let's call the distance for the first part "D1" (because calling it "part 1" would be too mainstream).
Now, we're told that the second part of the trip was 25 miles longer than the first part. So, the distance for the second part would be "D1 + 25" (because Marge couldn't resist making the trip a little more adventurous).
Next, we're told that the second part of the trip took 30 minutes longer than the first part. Now, converting minutes to miles might be a bit tricky unless Marge borrowed a time machine. So, let's convert those 30 minutes to hours by dividing it by 60: 30/60 = 0.5 hours. So, the time taken for the second part would be the time taken for the first part + 0.5 hours.
Now, let's use the formulas Distance = Speed × Time (I hope you remembered to buckle up your formula seatbelt!).
For the first part: D1 = 70 mph × Time1
For the second part: D1 + 25 = 60 mph × (Time1 + 0.5)
But wait, there's more! We also have another piece of information: Marge is a speed demon (just kidding), and her second part of the trip took 30 minutes longer than the first part. So, we can also say that Time1 + 0.5 = Time1 + 0.5 + 0.5 (because 30 minutes is equal to 0.5 hours).
Now, let's solve this circus of equations and find the solution!
70 mph × Time1 = 60 mph × (Time1 + 0.5)
70 mph × Time1 = 60 mph × Time1 + 60 mph × 0.5
70 mph × Time1 - 60 mph × Time1 = 30 mph × 0.5
(70 mph - 60 mph) × Time1 = 15 mph
10 mph × Time1 = 15 mph
Time1 = 15 mph / 10 mph
Time1 = 1.5 hours
Now that we know Time1 is 1.5 hours, we can find D1:
D1 = 70 mph × 1.5 hours
D1 = 105 miles
Since the second part of the trip was 25 miles longer, the distance for the second part would be:
D1 + 25 = 105 miles + 25 miles
D1 + 25 = 130 miles
Finally, the total distance to Carmel would be the sum of the distances for the two parts:
Total distance = D1 + D1 + 25
Total distance = 105 miles + 130 miles
Total distance = 235 miles
Voila! Marge had a wild and zigzagging adventure covering a total distance of 235 miles to reach Carmel. I hope she remembered to bring her sense of direction next time!
Let's denote the distance of the first part of the trip as "x" miles. According to the given information, Marge traveled at an average speed of 70 mph during this part.
Given that the second part of the trip was 25 miles longer than the first part, its distance can be expressed as "x + 25" miles. Marge traveled at an average speed of 60 mph during this part.
To find the total distance to Carmel, we need to add the distances of the two parts.
Total distance = distance of first part + distance of second part
Total distance = x + x + 25 [since the second part is 25 mi longer]
Total distance = 2x + 25
Now, let's determine the time it took for each part of the trip.
Time taken for the first part = distance / speed = x / 70
Time taken for the second part = distance / speed = (x + 25) / 60
We are given that the second part of the trip took 30 minutes more than the first part. Since 30 minutes is equal to 0.5 hours, we can set up the following equation:
(x + 25) / 60 = x / 70 + 0.5
Now, let's solve for x.
Multiply both sides of the equation by 60 and 70 to eliminate the denominators:
70(x + 25) = 60x + 30
70x + 1750 = 60x + 30
Simplify the equation:
10x = 1720
Divide both sides of the equation by 10 to solve for x:
x = 172
Now, let's find the total distance:
Total distance = 2x + 25
= 2 * 172 + 25
= 344 + 25
= 369 miles
Therefore, the total distance to Carmel is 369 miles.
To solve this problem, we need to break it down into several steps:
Step 1: Understand the given information.
From the problem, we know that Marge traveled at an average speed of 70 mph during the first part of the trip and 60 mph during the second part. We are also given that the second part of the trip took 30 minutes longer than the first part, and that the second part is 25 miles longer than the first part.
Step 2: Set up the equations.
Let's assume that the distance of the first part of the trip is represented by "x" miles. Since the second part is 25 miles longer, the distance of the second part is "x + 25" miles.
We can now use the formula: Time = Distance / Speed
For the first part of the trip, the time can be represented as "x / 70".
For the second part of the trip, the time can be represented as "(x + 25) / 60".
Since the second part took 30 minutes longer, we can write the equation: (x / 70) + 30/60 = (x + 25) / 60
Step 3: Solve the equation.
To solve the equation, we first multiply through by 70 to eliminate the denominators:
70(x / 70) + 70(30/60) = 70((x + 25) / 60)
x + 35 = (7x + 175) / 6
Next, we multiply both sides of the equation by 6 to eliminate the denominator:
6(x + 35) = 7x + 175
6x + 210 = 7x + 175
Now, we simplify the equation:
210 - 175 = 7x - 6x
35 = x
Step 4: Calculate the total distance.
Now that we know the distance of the first part is 35 miles, we can calculate the second part by adding 25 miles to it:
x + 25 = 35 + 25 = 60 miles
To find the total distance, we add the distances of the two parts:
Total distance = 35 + 60 = 95 miles
Therefore, the total distance to Carmel is 95 miles.
Since distance = speed * time,
70t + 25 = 60(t + 1/2)
t = 1/2
So,
70mi/hr for 1/2 hr = 35mi
60mi/hr for 1 hr = 60mi = 35+25 mi