19. Jim paddles from one shore of a lake three miles wide at 4 mph, and John paddles from the opposite shore at 5 mph. How long will they travel before they meet?
A. 20 minutes B. 27 minutes C. 1 hour, 24 minutes D. 3 hours
Jim is 1 mile away from John,so that means that it should take Jim at least an hour or two to get to John.I don't know if I expand this the right way.
Then this answer will have to be C or D for sure,if not please correct me.
Thank you any help is appreciated.
I believe the answer is A.
Also, please look at the first three Related questions for this problem.
I hope this helps! :)
Thanks
You're welcome, Sarah. I don't really know how to explain it, so once I saw this was in the Related Questions, I knew that an actual tutor would be better.
To solve this problem, we can use the concept of relative speed.
First, let's calculate how long it will take for Jim to cross the lake, which is three miles wide, at a speed of 4 mph. We can use the formula:
Time = Distance / Speed
So, for Jim:
Time = 3 miles / 4 mph
Time = 0.75 hours
Now, let's calculate how long it will take for John to cross the lake, which is again three miles wide, but at a speed of 5 mph:
Time = 3 miles / 5 mph
Time = 0.6 hours
Since Jim and John are paddling towards each other, their speeds add up. So, their combined speed is 4 mph + 5 mph = 9 mph.
To find out how long it will take for them to meet, we can use the same formula:
Time = Distance / Speed
In this case, the distance is the distance between the two shores, which is 3 miles. The combined speed is 9 mph.
Time = 3 miles / 9 mph
Time = 0.33 hours
To convert the time from hours to minutes, we multiply by 60:
Time = 0.33 hours * 60 minutes/hour
Time ≈ 19.8 minutes
Therefore, the answer is approximately 19.8 minutes, which is closest to 20 minutes. Hence, the correct answer is A.
Note: It's important to keep track of the units while performing calculations and consider the relative speed when the two individuals are moving toward each other.