The time, t, required to drive a certain distance varies inversely with the speed, r. If it takes 7 hours to drive the distance at 55 miles per hour, how long will it take to drive the same distance at 65 miles per hour?
• about 6.25 hours
• about 385.00 hours
• about 5.92 hours
• about 3.21 hours
Show how to get answer...
since ts = k is constant,
and 65 = 13/11 * 55,
(7)(55) = (11/13 * 7)(13/11 * 55)
11/13 * 7 = 5.92
It always help to see how it is done. Thanks.
To solve this problem, we can use the concept of inverse variation. In inverse variation, when one variable increases, the other variable decreases at a constant rate.
In this case, the time, t, is inversely proportional to the speed, r. This can be represented mathematically as t = k/r, where k is a constant.
We are given that it takes 7 hours to drive the distance at 55 miles per hour. Let's use this information to find the value of k.
Plugging in the given values, we have 7 = k/55. To find k, we can multiply both sides of the equation by 55: 7 * 55 = k, which gives us k = 385.
Now that we know the value of k, we can use it to solve the problem. We want to find the time it takes to drive the same distance at 65 miles per hour.
Plugging in the new value of r, we have t = 385/65. Simplifying this equation, we get t = 5.92.
Therefore, it will take about 5.92 hours to drive the same distance at 65 miles per hour. So, the correct answer is option C: about 5.92 hours.
you can also see that since st is constant,
65t = 55*7