Tony is 1/2 of a mile ahead of Laura on a jogging path. If Tony is running at 5 miles per hour, and Laura is running at 7 miles per hour, how long will it take Laura to catch up with Tony?
To find out how long it will take Laura to catch up with Tony, we need to determine the time it will take for Laura to travel the same distance as Tony.
First, let's calculate Tony's speed in miles per minute. We know Tony is running at 5 miles per hour, so his speed in miles per minute is:
5 miles/hour * 1/60 hours/minute = 1/12 miles/minute
Let's define t as the time it will take for Laura to catch up with Tony in minutes. In that time, Tony will have covered a distance of:
(1/12 miles/minute) * t minutes = t/12 miles
Since Tony is already 1/2 mile ahead of Laura, his total distance covered will be:
t/12 miles + 1/2 miles
Now, let's calculate Laura's speed in miles per minute. We know Laura is running at 7 miles per hour, so her speed in miles per minute is:
7 miles/hour * 1/60 hours/minute = 7/60 miles/minute
In the same time t, Laura will have covered a distance of:
(7/60 miles/minute) * t minutes = 7t/60 miles
We want to find the time t when Laura and Tony will cover the same distance, so we can set up the equation:
t/12 miles + 1/2 miles = 7t/60 miles
Now we can solve for t:
Multiply both sides of the equation by 60 to get rid of the denominators:
60(t/12 miles + 1/2 miles) = 60(7t/60 miles)
5t + 30 = 7t
Subtract 5t from both sides:
30 = 2t
Divide both sides by 2:
t = 15
Therefore, it will take Laura 15 minutes to catch up with Tony.