John was jogging at a rate of 5mph and he has a one half mile start on Sue who jogs at 7 mph. In how many minutes will it take before they meet?
Sue is 2 mi/hr faster. So, how long to make up the 1/2 mile?
To solve this problem, we need to determine the time it takes for John and Sue to meet while jogging. Here's how we can approach it:
Step 1: Convert John's speed from mph (miles per hour) to miles per minute. Since we need the time in minutes, this conversion will help us keep the units consistent.
John's speed = 5 mph
John's speed in miles per minute = 5/60 = 1/12 miles per minute
Step 2: Calculate the relative speed between John and Sue. Since John has a half-mile head start, the relative speed between them is the difference between their individual speeds.
Relative speed = 7 mph (Sue's speed) - 5 mph (John's speed) = 2 mph
Step 3: Calculate the time it takes for John and Sue to meet. We can use the formula "Time = Distance / Speed."
Distance = half a mile (John's head start) = 1/2 mile
Speed = relative speed = 2 mph
Time = (1/2) / 2 = 1/4 hour
Step 4: Convert the time from hours to minutes. Since we need the time in minutes, multiply the time by 60.
Time in minutes = (1/4) * 60 = 15 minutes
Therefore, it will take John and Sue 15 minutes to meet while jogging.