Solve for x. x/5 = 20
2 answers:
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Answer: 5 minutes or 1/12 hour
Explanation:
Let t = time it takes for Alex to catch up with Victor.
s = time it took for Victor to ride 1/2 km
Note that Alex will only start catching up with Victor when he already traveled the same distance with Victor. In terms of equation:
distance traveled by Alex = distance traveled by Victor
(speed of Alex)(time of Alex) = (speed of victor)(time of victor) (1)
Note: The amounts of time indicated in equation (1) refer to the amounts of time they spent on riding a bike when Alex catches up with Victor.
Since the speeds of Alex and Victor are given in the problem, we need to figure out the amount of time stated in equation (1).
Since Alex started to ride his bike only when Victor already traveled 1/2 km using his bike and Victor has already elapsed time s in riding 1/2 km, Alex only started to bike at time s. So Victor has elapsed a time of (t + s) riding a bike when he is caught up by Alex.
Using equation (1),
(speed of Alex)(time of Alex) = (speed of victor)(time of victor)
24t = 18(t + s) (2)
To solve for s, recall that we'll use the following formula
distance = (speed)(time)
Substituting this value of s to equation (1), we have
24t = 18(t + 1/36)
24t = 18t + 18(1/36)
24t = 18t + 1/2
6t = 1/2
(6t ÷ 6) = (1/2) ÷ 6
t = 1/12 hour (Since the unit for speed in the problem is km/hr)
We can convert 1/12 hour to minutes by multiplying 1/12 by 60 since 1 hour = 60 minutes. So, t = 5 minutes. Hence, it will take 5 minutes for Alex to catch up with Victor.
Explanation:
Let t = time it takes for Alex to catch up with Victor.
s = time it took for Victor to ride 1/2 km
Note that Alex will only start catching up with Victor when he already traveled the same distance with Victor. In terms of equation:
distance traveled by Alex = distance traveled by Victor
(speed of Alex)(time of Alex) = (speed of victor)(time of victor) (1)
Note: The amounts of time indicated in equation (1) refer to the amounts of time they spent on riding a bike when Alex catches up with Victor.
Since the speeds of Alex and Victor are given in the problem, we need to figure out the amount of time stated in equation (1).
Since Alex started to ride his bike only when Victor already traveled 1/2 km using his bike and Victor has already elapsed time s in riding 1/2 km, Alex only started to bike at time s. So Victor has elapsed a time of (t + s) riding a bike when he is caught up by Alex.
Using equation (1),
(speed of Alex)(time of Alex) = (speed of victor)(time of victor)
24t = 18(t + s) (2)
To solve for s, recall that we'll use the following formula
distance = (speed)(time)
Substituting this value of s to equation (1), we have
24t = 18(t + 1/36)
24t = 18t + 18(1/36)
24t = 18t + 1/2
6t = 1/2
(6t ÷ 6) = (1/2) ÷ 6
t = 1/12 hour (Since the unit for speed in the problem is km/hr)
We can convert 1/12 hour to minutes by multiplying 1/12 by 60 since 1 hour = 60 minutes. So, t = 5 minutes. Hence, it will take 5 minutes for Alex to catch up with Victor.
Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period. This is calculated using:
Where:
So, we have:
Solving (b): The maximum and the minimum height
To do this, we have:
Which means:
So, the minimum is:
And the maximum is:
Recall that the height is:
So, the maximum and the minimum of are:
and