David drove 70 miles in the first 1 ¾ hours of his trip. How much longer should it take him to drive an additional 120 miles if he drives at the same average speed?
To find out how long it takes David to drive 1 mile, we divide the distance (70 miles) by the time (1 ¾ hours):
70 miles / 1 ¾ hours = 40 miles/hour.
To find out how long it takes David to drive 120 miles, we divide the distance (120 miles) by the average speed (40 miles/hour):
120 miles / 40 miles/hour = 3 hours.
It should take him an additional 3 hours to drive 120 miles.
To find out how much longer it should take David to drive an additional 120 miles, we need to determine his average speed and then calculate the time it would take to travel that distance.
Step 1: Find David's average speed
Average speed = total distance / total time
David drove 70 miles in 1 ¾ hours.
To calculate the average speed, we need to convert 1 ¾ hours to a decimal.
1 ¾ hours = 1.75 hours
Average speed = 70 miles / 1.75 hours
Average speed = 40 miles per hour
Step 2: Calculate the time it would take to travel an additional 120 miles.
Time = distance / speed
Distance = 120 miles
Speed = 40 miles per hour
Time = 120 miles / 40 miles per hour
Time = 3 hours
Therefore, it should take David an additional 3 hours to drive 120 miles at the same average speed.