Paula leaves home driving 40 miles/hr. One hour later Dan leaves home driving in the same direction at the rate of 50 miles/hr. How long will it take dan to catch up with Paula?
To find out how long it will take Dan to catch up with Paula, we need to determine the distance Paula travels before Dan starts his journey.
Since Paula is driving at a speed of 40 miles/hr and she starts one hour earlier than Dan, we can calculate the distance she travels using the formula:
Distance = Speed × Time
Distance = 40 miles/hr × 1 hour = 40 miles
Now, we know that Dan is driving at a speed of 50 miles/hr and needs to catch up with Paula, who has already traveled 40 miles. To determine how long it will take Dan to catch up, we can use the formula:
Time = Distance / Speed
Time = (40 miles) / (50 miles/hr) = 0.8 hours
Therefore, it will take Dan 0.8 hours (or 48 minutes) to catch up with Paula.
To find out how long it will take Dan to catch up with Paula, we need to determine the time it takes for Dan to cover the same distance that Paula has already covered.
Let's assume that the distance Paula has already covered when Dan starts is represented by D distance units.
Since Paula is driving at a speed of 40 miles/hr, her distance covered after one hour can be calculated as follows:
Distance covered by Paula = Speed * Time
Distance covered by Paula = 40 miles/hr * 1 hr
Distance covered by Paula = 40 miles
Now, let's find out how long it will take Dan to cover this distance.
Since Dan is driving at a speed of 50 miles/hr, the time required for him to cover the distance D can be calculated as follows:
Time taken by Dan = Distance / Speed
Time taken by Dan = D / 50 miles/hr
Since Dan needs to catch up with Paula, the distance D covered by Paula and the distance covered by Dan after the same amount of time must be the same.
Therefore, we can set up the following equation to find D:
D = Distance covered by Paula = 40 miles
Now, we can calculate the time it will take Dan to catch up with Paula:
Time taken by Dan = D / 50 miles/hr
Time taken by Dan = 40 miles / 50 miles/hr
Time taken by Dan = 0.8 hr
So, it will take Dan 0.8 hours (or 48 minutes) to catch up with Paula.