It takes Ross, traveling at 24 mph, 10 minutes longer to go a certain distance than it takes Evelyn traveling at 30 mph. Find the distance traveled

To find the distance traveled, we need to first calculate the time taken by both Ross and Evelyn.

Let's assume the distance traveled is "d" miles.

Evelyn's speed is 30 mph, so the time taken by Evelyn to travel the distance is given by the formula:

Time = Distance / Speed
Time taken by Evelyn = d / 30

Ross's speed is 24 mph, and it takes him 10 minutes (or 10/60 = 1/6 hours) longer than Evelyn. So, the time taken by Ross is:

Time taken by Ross = Time taken by Evelyn + 1/6
Time taken by Ross = (d / 30) + 1/6

Since we know that Ross's time is 10 minutes longer than Evelyn's time, we can set up the following equation:

(d / 30) + 1/6 = d / 24

To solve this equation, we can multiply through by the least common multiple of the denominators (30 and 24), which is 120:

120*(d / 30) + 120*(1/6) = 120*(d / 24)
4d + 20 = 5d

To isolate "d" on one side of the equation, we can subtract 4d from both sides:

20 = d

Therefore, the distance traveled is 20 miles.

To find the distance traveled, we need to first determine the time it takes for each person to travel the distance.

Let's assume the distance traveled is represented by "d" (in miles).

For Ross, traveling at 24 mph, the time taken can be calculated using the formula:

Time = Distance / Speed

t1 = d / 24

Similarly, for Evelyn, traveling at 30 mph, the time taken can be calculated using the same formula:

t2 = d / 30

According to the given information, it takes Ross 10 minutes longer to travel the distance compared to Evelyn. Since there are 60 minutes in an hour, we can convert the 10 minutes to fractional hours:

10 minutes = 10/60 = 1/6 hours

So, we can say that t1 = t2 + 1/6.

Now, we can substitute the expressions for t1 and t2 in terms of d into the equation:

d / 24 = d / 30 + 1/6

To solve this equation, we can multiply both sides by 120 (the least common multiple of 24 and 30) to get rid of the denominators:

120 * (d / 24) = 120 * (d / 30) + 120 * (1/6)

5d = 4d + 20

Subtracting 4d from both sides, we get:

d = 20

Therefore, the distance traveled, represented by "d," is 20 miles.

Since time = distance/speed,

d/24 + 1/6 = d/30