Question 46713: Two riders on bicycles, 100 miles apart, begin traveling toward each other at the same time, one traveling at 10 mph and the other at 15 mph. A fly begins flying between the bicycles, starting from the front wheel of the slower bicycle. If the fly travels at 20 mph flying back and forth between bicycles, being able to reverse directions without losing any time, how far will the fly tarvel before the bicycles meet?
HERE IS A COPY OF WHAT I HAVE ATTEMPTED:
Step 1
Now you need to identify the unknown. An unknown is a quantity that you problem requires you to find out, or the quantity that is necessary to find out in order to obtain the solution.
What is the unknown in this problem?
There are several ways to define the unknown in this problem. We are using one of them. They all lead to the same result.
Please choose one answer.
o The time of their trip, and the distance from where they start to the point of their meeting.
o The difference between their speeds
You should have chosen the time of their trip.
Since the time of the trip is what the problem asks for, you can choose it as your unknown in this case. Note that for other problems, it may be more convenient to choose something else as the unknown, calculate its value, and then use it to come up with the answer to the problem.
Step 2: Now you need to find out the equation needed to solve the problem. The critical piece that you need is the fact that the two riders are at one point at the same time at the moment when they meet. Let’s denote the distance from the Start of the boy rider to that point as X. The distance from the girl to that point is 100-X.
The time t1 it takes the boy to reach the meeting point is x divided by his speed.
The time t2 it takes the girl to reach the meeting point is 100-X divided by its speed.
Since both riders are in the meeting point at the same time, these two times are equivalent. That is, t1=t2.
Please choose one answer.
o x/10 = (100-x)/15
o x/10 = x/15
Given the equation
x/10 = (100-x)/15,
we can simplify it as x/10 + x/15 = 100/15, or
x=10*100/(10+15)=40
The time that it takes the boy to travel 40 miles, is x divided by the speed he is going, which is
t=x/10=4
So, the answer is: 4 hours for the two riders to meet.
Now we have to figure Mr. Fly into the problem.
Now we have to find out how far Mr. Fly will travel before boy meets girl.
So far we know that Boy is going 10 mph so in 4 hours how far will he have gone?
Equation: 10mph * 4hrs = 40miles
Now MR. Fly is going 20mph and he is going back and forth between the boy and the girl. Mr. Fly is starting with the slower rider which is the boy going 10 mph. We need to find out how far Mr. Fly travels before boy and girl meet.
So let’s first find out how long and how far Mr Fly will travel before he meets Girl for the first time and then find out how far he went to make that first contact with Girl.
Now you need to find out the equation needed to solve the problem. The critical piece that you need is the fact that the Fly and the Girl area at one point on the line at the same time at the moment when the meet. Let’s denote the distance from Fly to that point as X. The distance from Girl to that point, is of course, 100-X.
The time t1 it takes the Fly to reach the meeting point is x divided by its speed.
The time t2 it takes the Girl to reach the meeting point is 100-X divided by her speed.
Since both trains are in the meeting point at the same time, these two times are equivalent. That is, t1=t2.
x/20 = (100-x)/15
we can simplify it as x/20 + x/15 = 100/15 or
x = 20 * 100/ (20=15) = 57.14 miles
The time that it takes the fly to travel 57.14 miles, is x divided by the speed of Mr Fly, which is
t = x/20 = 2.86 hours
The Fly is in front of the Boy. The Boy is going 10mph which is half the speed of the fly. So how far did the boy travel in 2.86 hrs?
10 mph * 2.86 = 28.6 miles
Girl went 42.86 miles
So in 2.86 hours the Boy went 28.6 miles. Mr Fly bounces off of Girl and immediately starts Flying back to the Boy. Do you know how far apart the Fly is from the Boy when Mr Fly bounces off of the Girl?
57.14 – 28.6 = 28.54
Mr Fly is flying at 20mph towards Boy who is going 10mph. There is 28.54 miles in between them.
What equation would we use?
The critically piece that you need is the fact that the Boy and Fly are at one point at the same time at the moment when they meet. Let’s denote the distance from Boy to that point as x. The distance from Fly to that point is, of course, 28.54-x.
The time t1 takes the Boy to reach the meeting point is x divided by its speed.
The time t2 it takes the Fly to reach the meeting point is 28.54-x divided by its speed
Since both trains are in the meeting point at the same time, these two times are equivalent. That is, t1 = t2.
x/10 = (28.54 – x) /20
we can simplify it as x/10 + x/20 = 28.54/20 or
x = 10 * 28.54 / (10 + 20) = 9.51
The time that it takes the Boy to travel 9.51 miles, is x divided by the speed of the Boy, which is
T = x / 10 = .951 hours.
So far Mr Fly has traveled 28.54 miles plus 9.51 miles = 38.05mi
Answer by Paul(988)   (Show Source):
You can put this solution on YOUR website! Whoa your attempt is really lengthy.
Ok, first find the time it will take the bicyles to meet
so thats
10x+15x=100
x=4
In 4 hours the bicyles will meet.
SO 4(20)=80
SO the fly would have travelled 80 miles by then.
Paul.
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