Tom leaves the outskirts of City A at 8 am and travels north to City B at a constant speed of 80 km/h. Cindy leaves from the same place at 8:30 am and takes the same route traveling at a constant speed of 100 km/h. At what time will Cindy overtake Tom along the road to City B?
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To find out at what time Cindy will overtake Tom, we can determine the distance Tom travels before Cindy starts and the time it takes for Cindy to catch up with Tom.
Let's start by finding out the time it takes for Tom to travel before Cindy starts. Cindy starts 30 minutes (or 0.5 hours) after Tom.
To find the distance Tom covers in that time, we'll use the formula distance = speed * time. Tom's speed is given as 80 km/h, and the time he travels before Cindy starts is 0.5 hours.
distance covered by Tom = 80 km/h * 0.5 h = 40 km
Therefore, when Cindy starts, Tom will be 40 kilometers ahead.
Now, let's determine the time it takes for Cindy to catch up with Tom. To calculate this, we'll use the following formula:
time = distance / relative speed
The relative speed is the difference between Cindy's speed and Tom's speed. So,
relative speed = Cindy's speed - Tom's speed
relative speed = 100 km/h - 80 km/h = 20 km/h
Using this relative speed, we can calculate the time it takes for Cindy to catch up with Tom:
time = 40 km / 20 km/h = 2 hours
Since Cindy starts 30 minutes (or 0.5 hours) later, we need to add this time to the time it takes for Cindy to catch up:
total time = 2 hours + 0.5 hours = 2.5 hours
Therefore, Cindy will overtake Tom 2.5 hours after she starts, or at 8:30 am + 2.5 hours = 11:00 am.