Hi,
Would you please check to see if I did this problem correctly?
Your distance from lightning varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see the lightning, you are about 2 miles from the lightning.
a. Write a direct variation equation for the relationship between time and distance.
d = distance from lightning
t = time it takes you to hear the lightning
d = kt
2 = k10
k = 20
So, d = 20t
b. Estimate how many seconds it would take for the thunder to travel a distance of 4 miles.
4 = 20t
t = 80 miles
Thank you
d = kt
3 = 10k
k = 1/5
d = t/5
that is, 1/5 mile for every second of elapsed time
the time should not be in MILES
right, 80 seconds. Thank you
To check if your solution is correct, let's work through the problem together.
a. In a direct variation, the equation is y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation. In this case, the distance (d) is the dependent variable, and the time (t) is the independent variable.
So, the equation for the direct variation relationship between time (t) and distance (d) is:
d = kt
You correctly set d = 2 miles and t = 10 seconds, and solved for k. By substituting these values into the equation, you obtained:
2 = k * 10
Simplifying, we get:
k = 2/10 = 0.2
Therefore, the correct equation for the relationship between time and distance is:
d = 0.2t or d = 20t (if units are in miles and seconds).
b. To estimate how many seconds it would take for the thunder to travel a distance of 4 miles, we can use the equation from part (a):
d = 20t
To find t, we substitute d = 4 miles into the equation:
4 = 20t
Solving for t:
t = 4/20 = 0.2 hours
To convert hours to seconds, we multiply by 60 minutes per hour and 60 seconds per minute:
t = 0.2 * 60 * 60 = 720 seconds
So, it would take approximately 720 seconds for the thunder to travel a distance of 4 miles.
Checking your solution, you made an error in part (b) by stating that t = 80 miles instead of 80 seconds. The correct answer is t = 720 seconds.
I hope this helps! Let me know if you have any further questions.