Starting from 105 feet away, a person on a bicycle rides towards a checkpoint and then passes it. The rider is traveling at a constant rate of 35 feet per second. The distance between the bicycle and the checkpoint is given by the equation d = 105 - 35t. At what times is the bike 60 feet away from the checkpoint?
A: 1.3 sec and 2.6 sec
B: 1.3 sec and 4.7 sec*
C: 1.1 sec and 2.6 sec
D: 4.7 sec and 9.4 sec
I honestly took a wild guess since I have no idea to start. Any feedback would be insanely helpful and needed. Thank you!
consider that the rider will be 60 feet away both approaching and receding. So, you want
|105-35t| = 60
for positive distance (still approaching),
105-35t = 60
t = 9/7 = 1.28
Going away, you have
105-35t = -60
t = 33/7 = 4.71
http://www.wolframalpha.com/input/?i=%7C105-35t%7C+%3D+60
Anyone have all the answers
To find the times when the bike is 60 feet away from the checkpoint, we need to substitute the equation for distance (d) into the given equation:
d = 105 - 35t
Substituting in the value of 60 for d, we get:
60 = 105 - 35t
To solve for t, we rearrange the equation:
35t = 105 - 60
35t = 45
Now, divide both sides of the equation by 35:
t = 45/35
t = 1.2857 (approximately)
So, one of the times when the bike is 60 feet away from the checkpoint is approximately 1.3 seconds.
To find the second time, we can substitute the value of 60 into the original equation and solve for t again:
d = 105 - 35t
60 = 105 - 35t
Rearranging the equation:
35t = 105 - 60
35t = 45
Dividing both sides by 35:
t = 45/35
t = 1.2857 (approximately)
So, the second time when the bike is 60 feet away from the checkpoint is also approximately 1.3 seconds.
Therefore, the correct answer is A: 1.3 sec and 2.6 sec.
To find at what times the bike is 60 feet away from the checkpoint, we can substitute d = 60 into the equation d = 105 - 35t and solve for t.
Step 1: Substitute d = 60 into the equation d = 105 - 35t.
60 = 105 - 35t
Step 2: Simplify the equation by subtracting 105 from both sides.
-45 = -35t
Step 3: Divide both sides of the equation by -35.
t = (-45)/(-35)
t ≈ 1.2857
So, the bike is 60 feet away from the checkpoint at approximately 1.2857 seconds.
Now, let's check the given answer choices using this calculated result to determine the correct options.
A: 1.3 sec and 2.6 sec
B: 1.3 sec and 4.7 sec*
C: 1.1 sec and 2.6 sec
D: 4.7 sec and 9.4 sec
From the calculated result, we see that the bike is approximately 60 feet away from the checkpoint at 1.2857 seconds. The only option that includes this time is B: 1.3 sec and 4.7 sec, so the correct answer is B.