Rachel and Lindsay are in third place in a race. Due to a time penalty, they must start the next leg 90 minutes after the second place team. If rachel and lindsay travel at an average rate of 16.8 mph and the second place team travels at an average rate of 14 mph, how long will it take the girls to catch up to the second place team?
setting the distances equal, and assuming that the 2nd place team runs t hours,
14t = 16.8(t-1.5)
14t = 16.8t - 25.2
2.8t = 25.2
t=9
So, it will take 7.5 hours to catch up.
To solve this problem, we can first figure out how far ahead the second place team is from Rachel and Lindsay, and then calculate how long it will take for Rachel and Lindsay to close that distance.
Let's start by determining the distance the second place team will travel during the 90 minutes that Rachel and Lindsay must wait. We can use the formula:
Distance = Speed × Time
The speed of the second place team is given as 14 mph, and the time they have to travel is 90 minutes. However, we need to convert this time to hours since the speed is given in mph. There are 60 minutes in an hour, so 90 minutes equal 90/60 = 1.5 hours.
Calculating the distance:
Distance = 14 mph × 1.5 hours
Distance = 21 miles
Now that we know the distance between the two teams, we can determine how long it will take for Rachel and Lindsay to catch up. We will use the formula:
Time = Distance / Speed
The distance is 21 miles, and the speed of Rachel and Lindsay is given as 16.8 mph.
Calculating the time:
Time = 21 miles / 16.8 mph
Time ≈ 1.25 hours
Thus, it will take Rachel and Lindsay approximately 1.25 hours to catch up to the second place team.
To find out how long it will take Rachel and Lindsay to catch up to the second place team, we can use the formula:
Time = Distance / Speed
Let's first calculate the distance that the second place team will cover in 90 minutes:
Distance = Speed * Time
Distance = 14 mph * 90 minutes
To convert minutes to hours, we divide by 60:
Distance = 14 mph * (90 minutes / 60 minutes/hour)
Distance = 14 mph * 1.5 hours
Distance = 21 miles
Now that we have the distance, we can calculate how long it will take Rachel and Lindsay to cover the same distance:
Time = Distance / Speed
Time = 21 miles / 16.8 mph
Time ≈ 1.25 hours
To convert hours to minutes, we multiply by 60:
Time ≈ 1.25 hours * 60 minutes/hour
Time ≈ 75 minutes
Therefore, it will take Rachel and Lindsay approximately 75 minutes to catch up to the second place team.