Shelby leaves her house at 9 a.m. on her bike at a speed of 320 meters per minute. At 10:30 a.m. her brother, Colby, leaves the house on his bike and tries to catch up with Shelby. Colby rides at a speed of 500 meters per minute. At what time will Colby catch up with Shelby?
Let the time from 9:00 am until Colby catches her be t minutes
distance covered by Shelby in that time = 320t metres
distance covered by Colby in that time = 500(t - 90)
but they went the same distance, so
500(t-90) = 320t
......
t = 250 minutes or 4 hours and 10 minutes
So he catches up to her at 1:10 pm
check: Shelby went at 320 metres/minute for 250 minutes = 80,000 metres
Colby went for 160 minutes (13:10 - 10:30) at 500 m/min = 80,000 metres
Well, it sounds like Colby has some major catching up to do! With Shelby already ahead, it might take him a while. But fear not, my friend, for I shall calculate the time it will take for Colby to catch up!
Let's start by determining the time difference between Shelby and Colby. By the time Colby sets off, it's already 10:30 a.m., which is 1.5 hours after Shelby left.
Now, we need to find out how far Shelby has traveled in that time. She's been riding at a speed of 320 meters per minute for 1.5 hours, which is equal to 320 meters/minute * 90 minutes = 28,800 meters.
So, when Colby starts pedaling, Shelby is already 28,800 meters ahead of him.
To catch up, Colby needs to cover this distance while riding at a speed of 500 meters per minute. The time it will take him can be calculated as follows:
Time = Distance / Speed
Time = 28,800 meters / 500 meters per minute
Time ≈ 57.6 minutes
So, it will take Colby approximately 57.6 minutes to catch up with Shelby.
To find the exact time, we add these 57.6 minutes to the time when Colby starts, which is 10:30 a.m. So, we get:
10:30 a.m. + 57.6 minutes ≈ 11:27 a.m.
Voila! According to my calculations, Colby should catch up with Shelby at around 11:27 a.m. Now, let's hope he doesn't show up fashionably late with a flat tire!
To find the time when Colby catches up with Shelby, let's start by determining the time difference between their departures.
Shelby leaves the house at 9 a.m., and Colby leaves at 10:30 a.m. This means that Colby starts 1 hour and 30 minutes (or 1.5 hours) later than Shelby.
Since Shelby's speed is given in meters per minute, we need to convert the time difference to minutes: 1.5 hours x 60 minutes/hour = 90 minutes.
Now that we know the time difference, let's calculate the distance Shelby covers in this time.
Shelby's speed is 320 meters per minute, so in 90 minutes, she covers a distance of 320 meters/minute x 90 minutes = 28,800 meters.
Now let's determine the time it takes for Colby to catch up with Shelby.
Colby's speed is given as 500 meters per minute, and he needs to cover the distance of 28,800 meters.
Time = Distance / Speed = 28,800 meters / 500 meters per minute = 57.6 minutes.
Now, let's add this time to Colby's departure time to find out when he catches up with Shelby.
10:30 a.m. + 57.6 minutes = 11:27.6 a.m.
Therefore, Colby will catch up with Shelby at approximately 11:27.6 a.m.
To solve this problem, we need to find the time it takes for Colby to catch up with Shelby.
Let's begin by calculating how far Shelby has traveled when Colby starts.
From 9 a.m. to 10:30 a.m., Shelby has been riding for 1 hour and 30 minutes, which is equivalent to 90 minutes.
Shelby's speed is given as 320 meters per minute, so in 90 minutes, she will have traveled a distance of:
Distance = Speed × Time
Distance = 320 meters/minute × 90 minutes
Distance = 28,800 meters
Therefore, when Colby starts riding, Shelby is already 28,800 meters ahead of him.
Now we can find the time it takes for Colby to catch up with Shelby.
Let's assume it takes 't' minutes for Colby to catch up.
During this time, Shelby and Colby will be traveling at their respective speeds.
Shelby's distance = 28,800 + (320 × t) (traveling at a constant speed)
Colby's distance = 500 × t (traveling at a constant speed)
Since they both meet at the same point, Shelby's and Colby's distances will be equal.
28,800 + (320 × t) = 500 × t
Now, we can solve this equation to find the value of 't':
28,800 + 320t = 500t
Subtracting 320t from both sides:
28,800 = 500t - 320t
180t = 28,800
Dividing both sides by 180:
t = 28,800 / 180
t = 160
Therefore, it will take Colby 160 minutes to catch up with Shelby.
To find the time at which Colby catches up with Shelby, we need to add this time to Colby's starting time, which is 10:30 a.m.
If Colby starts at 10:30 a.m. and it takes him 160 minutes to catch up, he will catch up with Shelby at:
10:30 a.m. + 160 minutes = 12:10 p.m.
Therefore, Colby will catch up with Shelby at 12:10 p.m.