I cannot figure out what the answer to this problem is. Can somebody help plz? any help is greatly appreciated!
Tony swims 100 m downstream in 175 seconds. It takes him 400 seconds to swim back upstream.
5. Find Tony's rate with the current. I got r+c=175, where r=Tony's rate and c=rate of current.
6. Find Tony's rate against the current. I got r-c=400.
7. Find Tony's rate with no current.
8. Find the rate of the current.
9. What are the total distance and total time?
10. Find Tony's average speed.
Ok, I tried the addition method thing where you add r+c=175 to r-c=400 and you get 2r=575 which equals r=287.5, but it isn't possible. Can somebody help? I might be able to figure out problems 8.-10., but I don't get problem 7. Oh, and one more question...what would be the units for his average speed? Would it be meters/seconds?
Thank you very very very much!
try doing what tonyt did and count the time it takes
uh... what do you mean by that?
make a chart and it becomes very easy
-------------Dist------Rate-----Time
upstream---400(r+c)m---r+c m/s---400 sec
downstream-175(r-c)m---r-c m/s---175 sec
but we know the distance is 100 m, so...
400(r+c)=100
175(r-c)=100
r+c=1/4 I divided by 100
r-c= 4/7 I divided by 175
add these two
2r=23/28
r=23/56 m/s or .411 m/s
sub back to get c=.161 m/s
To solve problem 5, which asks for Tony's rate with the current, you correctly set up the equation r+c=175, where r represents Tony's rate and c represents the rate of the current. However, there seems to be a mistake in your calculations.
To find Tony's rate with the current, you need to solve the system of equations that you set up using the given information. Let's start by reinterpreting the equations:
Equation 1: r + c = 175 (Tony's rate plus the rate of the current equals the time it took him to swim downstream)
Equation 2: r - c = 400 (Tony's rate minus the rate of the current equals the time it took him to swim upstream)
To solve these equations, you have a few options. One method is to use the addition or elimination method, where you add or subtract the two equations to cancel out one of the variables. Since the coefficients of c in both equations are the same (1 and -1), you can safely add the equations:
(r + c) + (r - c) = 175 + 400
Simplifying this equation gives you:
2r = 575
Now, to find the value of r, you divide both sides of the equation by 2:
r = 287.5 m/s
However, upon further analysis, it seems like there might be an error in the given information. If Tony's rate is indeed 287.5 m/s, it would mean that he is an extremely fast swimmer, which seems unlikely. Therefore, it is possible that there might be a mistake in the given values or the calculations.
Moving on to problem 7, which asks for Tony's rate with no current, you can use the same approach. Recall that the equation r + c = 175 represents Tony's rate with the current. If you want to find Tony's rate with no current, you simply set the rate of the current (c) to 0 and solve the equation:
r + 0 = 175
r = 175 m/s
So Tony's rate with no current is 175 m/s.
For problem 8, which asks for the rate of the current, you can simply subtract Tony's rate with no current from his rate with the current:
c = (r + c) - r
c = 175 - 287.5
c = -112.5 m/s
Interestingly, the negative value suggests that the current is flowing in the opposite direction to Tony's swimming. Therefore, it might be worth double-checking the given information or calculations to ensure accuracy.
For problem 9, which asks for the total distance and total time, you can calculate them using the values you obtained for Tony's rates. The total distance is the sum of the downstream and upstream distances:
Total distance = 100 + 100 = 200 m
The total time is the sum of the downstream and upstream times:
Total time = 175 + 400 = 575 seconds
Lastly, for problem 10, which asks for Tony's average speed, you can use the formula Average speed = Total distance / Total time:
Average speed = 200 m / 575 sec = 0.348 m/s
Therefore, the units for Tony's average speed would be meters per second (m/s).
In conclusion, it is crucial to carefully check the given information, equations, and calculations to ensure accuracy and determine if there might be an error.