You and a friend take turns driving on a 450 mile trip. Your friend drives for 3.5 hours at an average speed of 60 miles per hours. What must your average speed be for the remainder of the trip if you want to reach your hotel in 4 more hours?
3.5 * 60 = 210 miles
450 - 210 = 240 miles to go
240 / 4 = 60 mph
To solve this problem, we need to find out how many miles your friend has already driven and how many miles are left for you to drive.
Your friend has driven for 3.5 hours at an average speed of 60 miles per hour. To find out how many miles your friend has driven, we can use the formula: distance = speed × time.
Distance driven by your friend = 60 miles/hour × 3.5 hours = 210 miles.
Now, we can calculate the distance remaining for you to drive: 450 miles - 210 miles = 240 miles.
You have 4 more hours to reach your hotel, so you need to find out what average speed you must maintain to cover the remaining 240 miles in 4 hours.
To find the required average speed, we can use the formula: speed = distance ÷ time.
Required average speed = 240 miles ÷ 4 hours = 60 miles per hour.
Therefore, your average speed for the remainder of the trip must be 60 miles per hour to reach your hotel in 4 more hours.
To find out what your average speed must be for the remainder of the trip, we need to calculate how much distance is left after your friend's drive and divide it by the remaining time.
First, we need to calculate how much distance your friend covered.
Distance covered by your friend = Speed * Time
Distance covered = 60 miles/hour * 3.5 hours = 210 miles
Now, we can calculate the remaining distance after your friend's drive.
Remaining distance = Total distance - Distance covered by your friend
Remaining distance = 450 miles - 210 miles = 240 miles
Next, we can determine the remaining time available for you to reach the hotel.
Remaining time = Total time - Time your friend spent driving
Remaining time = 4 hours - 3.5 hours = 0.5 hours
Finally, we can find your required average speed for the remaining distance.
Average speed = Remaining distance / Remaining time
Average speed = 240 miles / 0.5 hours = 480 miles per hour
Therefore, to reach your hotel in 4 more hours, your average speed for the remainder of the trip must be 480 miles per hour.