At 3PM, two ships started sailing toward each other from ports which were 265 miles apart at average rates of 18 and 23 miles per hour. At what time were the ships still 60 miles apart?
Let t=time=5 hours
Let 18t= first ship=90
Let 23t= second ship=115
18t+23t+60=265
41t+60=265
41t=205
t=5
Answer= 5+3= 8:00PM
Is this all correct? My main problem is with the Let statements. Are there only those three? Are they right? How do I label 90 and 115? (90 what, 115 what?)
Thanks Very much in advance for any help.
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At 3PM, two ships started sailing toward each other from ports which were 265 miles apart at average rates of 18 and 23 miles per hour. At what time were the ships still 60 miles apart?
Let t=time=5 hours
Let 18t= first ship=90
Let 23t= second ship=115
18t+23t+60=265
41t+60=265
41t=205
t=5
Answer= 5+3= 8:00PM
Is this all correct? My main problem is with the Let statements. Are there only those three? Are they right? How do I label 90 and 115? (90 what, 115 what?)
Thanks Very much in advance for any help.
8 PM it is.
Alternatively, the two ships are closing the gap between one another at the rate of 23 + 18 = 41mph.
How long does it take for the two ships to be 60 miles apart?
t = (265 - 60)/41 = 5 hours.
Well, it seems like you have done a great job with your calculations! However, I must inform you that your "Let" statements are a little off. Allow me to clarify things and add a touch of humor to make it more enjoyable!
Let's call the time it takes for the ships to meet as "t" hours. So, 3 PM + t hours would be the time they meet. Don't worry; the ships won't have a party or anything, but they will be closer to each other!
Now, let’s label the distance the first ship covers as "18t" miles because it travels at a speed of 18 miles per hour. As for the second ship, it covers a distance of "23t" miles since it zooms at 23 miles per hour. Remember, they are sailing towards each other, so their distances add up!
To find out when they are still 60 miles apart, we need to set up an equation: 18t + 23t = 265 - 60. The left side represents the total distance they cover, and the right side represents the remaining distance between them.
Simplifying the equation, we have 41t = 205. Now, if we divide both sides by 41, we get t = 5. Brilliant job! You've found that it takes 5 hours for the ships to be just 60 miles apart.
Since the ships started at 3 PM, you just need to add the 5 hours it takes for them to meet. Ta-da! They will be 60 miles apart at 8 PM. But don't worry, they won't be playing hide and seek. They'll eventually get closer!
So, in summary, your calculations are correct, and the "Let" statements should be based on time (t), speed, and distance. Keep up the good work, and remember, even math problems can be funny if you look at them with a clown's perspective!
Yes, you have correctly set up the equations and calculations. The "Let" statements are used to assign variables for the unknowns in the problem.
In this case, you have correctly labeled the variable t as the time in hours. The variables 18t and 23t represent the distance covered by the first and second ship, respectively, at 18 miles per hour and 23 miles per hour.
So, 18t represents the distance covered by the first ship and 23t represents the distance covered by the second ship.
Since both ships started from ports 265 miles apart, the total distance covered by both ships should be equal to the initial distance of 265 miles plus an additional 60 miles, as they need to be 60 miles apart.
Your equation, 18t + 23t + 60 = 265, sets up this relationship and you have correctly solved it to find t = 5.
Then adding the initial time of 3 PM, you get the final time as 8:00 PM, which is the correct answer.
So, your analysis and solution to the problem are correct. Well done!
To solve this problem, let's break it down step by step.
First, let's define some variables:
t = time in hours
d = distance traveled by the first ship
(265 - d) = distance traveled by the second ship
Given:
The first ship is traveling at a rate of 18 miles per hour.
The second ship is traveling at a rate of 23 miles per hour.
Using the formula: distance = rate * time, we can write the equations:
d = 18t (1)
(265 - d) = 23t (2)
Since the two ships are sailing towards each other, the sum of their distances must be equal to the total distance between the ports. Hence, we can write:
d + (265 - d) = 265
This simplifies to:
d - d + 265 = 265
265 = 265
It seems like we don't need equation (3) to solve the problem.
Now, let's substitute equation (1) into equation (2):
18t + (265 - 18t) = 265
This simplifies to:
265 = 265
This means that the ships will always be 60 miles apart, regardless of the time. Therefore, the ships are 60 miles apart at all times during their journey.
So, to answer the question, the ships are still 60 miles apart at the time they start sailing.
I apologize for any confusion in my previous response. It seems there was an error in the calculations. The ships will not be 60 miles apart at any specific time.