I've been working on this for an hour and I know it's more simple than I'm making it. Please enlighten me.
Cyclist 1 is traveling at 20 mph, Cyclist 2 is traveling at 14 mph. How long before they're 15 miles apart?
I've tried to fill in a block diagram and work from there, but, I end up with too many variables.
The key concept here is that the time they bike is the same for both.
I will assume they are traveling in opposite directions.
Let x miles be the distance the first one went, then 15-x is the distance the second one went
time of first = x/20
time for the second = (15-x)/14
solve x/20 = (15-x)/14
by cross-multiplying.
once you have x, put x into x/20 for the time in hours.
( I got .44 hours or 26.5 minutes.)
checking for reasonableness of answer.
26.5 minute is approx 1/2 hour
in 1/2 hour the first one went 10 miles in one direction, while the other biker went 7 miles, for a distance between of 17 miles.
since I estimated slightly over the time of the answer, I expected my estimated distance to be higher also.
So I am confident about my answer)
Thank you; however, the cyclists were traveling in the same direction, leaving at the same time. Therefore, I'm afraid I'm still without an answer.
bob columm covered the first 12 miles in 4 hours. he then increased the speed by 2 miles per hour. if the total distance of the trip was 52 miles, how long did it take to finish the trip?
To find the time it takes for the two cyclists to be 15 miles apart, we can use the formula:
Distance = Speed × Time
Let's consider the situation: Cyclist 1 is traveling at 20 mph, and Cyclist 2 is traveling at 14 mph. We want to find out how long it will take for them to be 15 miles apart.
Let's assume that Cyclist 1 is ahead of Cyclist 2 at the start. As time passes, Cyclist 1 will continue to move ahead, while Cyclist 2 will try to catch up.
Now, let's break down the problem into steps:
Step 1: Determine the relative speed
To find the relative speed between the two cyclists, we subtract the speed of Cyclist 2 from the speed of Cyclist 1:
Relative speed = Speed of Cyclist 1 - Speed of Cyclist 2
In this case, the relative speed is:
Relative speed = 20 mph - 14 mph = 6 mph
Step 2: Calculate the time
Using the formula Distance = Speed × Time, we can rearrange it to solve for time:
Time = Distance / Relative speed
In this case, we want to find the time it takes for the two cyclists to be 15 miles apart:
Time = 15 miles / 6 mph
By performing the division, we can find the answer:
Time = 2.5 hours
Therefore, it will take 2.5 hours for the two cyclists to be 15 miles apart.
By following these steps and using the formula Distance = Speed × Time, we can solve similar problems where two objects are moving at different speeds and distances are involved.