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 40 miles per hour, how long will it take to drive the same distance at 55 miles per hour?
a. about 2.91 hours
b. about 160.0 hours
c. about 22.0 hours
d. about 5.50 hours
Huh???
The only one of those answers less than 4 hours is A!
I think its B
Good grief! How did you get 160 hours? Think, man!
I'm no good at math I don't now how to do this...
4 hours at 40 miles per hour
Wouldn't it take less time if drove faster?
*if you drove faster
No so D.
Thanks.
To solve this problem, we can use the concept of inverse variation. Inverse variation states that two quantities are inversely proportional to each other if their product is constant.
In this case, the time required to drive a certain distance is inversely proportional to the speed. This can be represented mathematically as:
t = k/r
where t is the time, r is the speed, and k is the constant of variation.
To find the value of k, we can use the given information. We are told that it takes 4 hours to drive the distance at 40 miles per hour. Plugging these values into the equation, we get:
4 = k/40
To solve for k, we can multiply both sides of the equation by 40:
4 * 40 = k
k = 160
Now that we have the value of k, we can use the equation to find the time required to drive the same distance at a different speed. In this case, we want to find the time when the speed is 55 miles per hour. Plugging this value into the equation, we get:
t = 160/55
t ≈ 2.91
Therefore, it will take about 2.91 hours to drive the same distance at 55 miles per hour. Therefore, the correct answer is option a. about 2.91 hours.