If speed varies inversely as the time it takes to drive and Kris take 5 hours driving at 55 mph, what speed will Martin need to drive if he wants to take 5 1/2 hours
50
Well, it seems that Martin wants to take longer than Kris. Maybe he's a fan of scenic routes or just enjoys taking his time. In any case, if Martin wants to take 5 and a half hours, we can find his required speed using the inverse variation formula. Since speed varies inversely with time, we can say that:
speed = k / time
Where k is the constant of variation. Now, let's plug in Kris' speed and time to find k:
55 mph = k / 5 hours
Solving for k, we get:
k = 275
Now, let's plug in the new time for Martin:
speed = 275 / 5.5 hours
Calculating:
speed = 50 mph
So, Martin will need to drive at approximately 50 mph to take 5 and a half hours. However, I must admit, he might miss out on some fast-paced fun and end up "speeding" in the opposite direction by taking longer.
To find the speed at which Martin needs to drive, we can use the concept of inverse variation.
Inverse variation means that as one variable increases, the other variable decreases, and vice versa. In this case, we are given that speed varies inversely with time. This means that as the time it takes to drive increases, the speed decreases.
We are given that Kris drives at a speed of 55 mph and takes 5 hours to drive. Let's define variables for speed (S) and time (T) for Martin's drive:
Let S be the speed at which Martin needs to drive.
Let T be the time it will take Martin to drive.
According to the inverse variation relationship, we can set up the equation:
Speed × Time = Constant
For Kris's drive: 55 mph × 5 hours = Constant
To find the constant, we can solve for it:
Constant = 55 mph × 5 hours = 275
Now, we can use this constant to find the speed Martin needs to drive. We know that he wants to take 5 1/2 hours, which is equivalent to 5.5 hours.
55 mph × 5.5 hours = Constant
Substituting the value of the constant we found earlier:
55 mph × 5.5 hours = 275
Now, let's solve for the speed S:
S = 275 / 5.5
Simplifying the expression, we get:
S = 50 mph
Therefore, Martin needs to drive at a speed of 50 mph if he wants to take 5 1/2 hours.
speed * time is constant, so you want x such that
5 1/2 x = 5*55