The time t required to drive a certain distance varies inversely with the speed r. If it takes 4 hours to drive the distance at 35 miles per hour, how long will it take to drive the same distance at 45 miles per hour?
A. about 3.11 hours
B. 140 hours
C. about 5.14 hours
D. 393.75 hours
The time t required to drive a certain distance varies inversely with the speed r. If it takes 4 hours to drive the distance at 35 miles per hour, how long will it take to drive the same distance at 45 miles per hour?
A. about 3.11 hours
B. 140 hours
C. about 5.14 hours
D. 393.75 hours
Using the inverse variation formula:
t = k/r
where t is the time, r is the speed, and k is a constant of proportionality.
To find k, plug in the given values:
4 = k/35
Solve for k:
k = 140
Now we can use k to find the time required at 45 miles per hour:
t = 140/45
t ≈ 3.11 hours
Therefore, the answer is A. about 3.11 hours.
or, in very simple steps:
distance driven = (4hrs)(35) mph = 140 km
time taken at 45 mph = 140 km/45 kmh = 3 1/9 hrs or 3.111.. hrs
Yes, that works too! Your method uses a more straightforward approach by finding the distance first and then dividing by the speed.
We are given that the time t required to drive a certain distance varies inversely with the speed r.
We can write this inverse variation relationship as t = k/r, where k is the constant of variation.
We are also given that it takes 4 hours to drive the distance at 35 miles per hour. So, we can substitute these values into the equation to find k:
4 = k/35
To solve for k, we can multiply both sides of the equation by 35:
35 * 4 = k
140 = k
Now we can use the value of k to find how long it will take to drive the same distance at 45 miles per hour:
t = k/r
t = 140/45
Calculating this, t ≈ 3.11 hours.
Therefore, the answer is A. about 3.11 hours.
To solve this problem, we first need to understand the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases, and vice versa.
In this problem, the time required to drive a certain distance (t) varies inversely with the speed (r). This can be represented by the equation t = k/r, where k is a constant.
We are given that it takes 4 hours to drive the distance at a speed of 35 miles per hour. Using this information, we can substitute these values into the equation and solve for k:
4 = k/35
To find k, we can multiply both sides of the equation by 35:
4 * 35 = k
k = 140
Now that we have the value of k, we can use it to find the time required to drive the same distance at a speed of 45 miles per hour. Substitute the values into the equation:
t = 140/45
Calculating the result gives us:
t ≈ 3.11 hours
Therefore, the correct answer is option A: about 3.11 hours.