Sue left her home at 6 A.M. driving her car at the rate of 50 miles per hour. At 8 A.M. her brother Kevin drove after her along the same highway, traveling at the rate of 60 miles per hour, in how many hours did Kevin pass Sue?
I got 10 hours but that is when they're at the same distance, so would the answer be 11?
he passes when they are at the same distance ... 10 is correct
To find out when Kevin passes Sue, we need to determine the time difference between their starts and the time it takes for Kevin to catch up to Sue.
Let's calculate the time difference between their starts:
Sue left at 6 A.M., and Kevin left at 8 A.M.
There is a time difference of 2 hours (8 A.M. - 6 A.M. = 2 hours).
Now, let's determine the time it takes for Kevin to catch up to Sue:
First, we need to consider that by the time Kevin starts driving, Sue has already been driving for 2 hours.
Next, we need to calculate the distance Sue travels in those 2 hours:
Distance = Speed × Time
Distance = 50 miles/hour × 2 hours
Distance = 100 miles
Now, since Kevin is driving faster than Sue at 60 miles per hour, it will take him less time to cover the same distance of 100 miles.
Time = Distance / Speed
Time = 100 miles / 60 miles/hour
Time ≈ 1.67 hours
Therefore, Kevin will pass Sue approximately 1.67 hours after he starts driving.
Now, to find the total time Kevin takes to pass Sue, we need to add the time difference between their starts (2 hours) to the time it takes for Kevin to catch up to Sue (1.67 hours):
Total Time = Time difference + Time taken to catch up
Total Time = 2 hours + 1.67 hours
Total Time ≈ 3.67 hours
Hence, Kevin will pass Sue in approximately 3.67 hours or about 3 hours and 40 minutes.
To determine at what time Kevin passes Sue, we need to find the time it takes for Kevin to catch up to Sue. Since Sue left at 6 A.M. and Kevin started at 8 A.M., Sue had a head start of 2 hours. During these 2 hours, Sue traveled at a rate of 50 miles per hour.
To find the distance Sue traveled during the 2-hour head start, we can calculate: distance = speed × time = 50 miles/hour × 2 hours = 100 miles.
So, when Kevin started, Sue was already 100 miles ahead of him.
Now, let's determine how long it takes for Kevin to catch up to Sue. Since Kevin's speed is 60 miles per hour and he needs to cover the 100-mile distance between them, we can calculate the time it takes for him to catch up to Sue: time = distance ÷ speed = 100 miles ÷ 60 miles/hour.
Using division, 100 ÷ 60 = 1.67 hours or rounded to the nearest whole number, it is 2 hours.
Therefore, Kevin will catch up to Sue 2 hours after he starts driving. Adding the initial 2-hour head start, the total time would be 4 hours.
Thus, Kevin will pass Sue 4 hours after he starts driving.