Joe can drive from his house to his office in 40 minutes at an average speed of 40 miles per hour. What average is needed to drive the same distance in half an hour? If necessary, round your answer to the nearest tenth.
Distance = Speed/time = 40/(2/3) = ?
?D = Speed/(1/2)
Calculate for distance, then speed.
To determine the average speed needed to drive the same distance in half an hour, we can use the formula:
Average speed = Distance / Time
Given that Joe can drive from his house to his office in 40 minutes (2/3 of an hour) at an average speed of 40 miles per hour, we can calculate the distance using the formula:
Distance = Speed x Time
Distance = 40 miles/hour x (2/3) hours
Distance = 80/3 miles
To find the average speed needed to drive the same distance in half an hour (1/2 hour), we substitute the distance and time into the formula:
Average speed = (80/3) miles / (1/2) hour
Using division of fractions, we can multiply by the reciprocal:
Average speed = (80/3 miles) * (2/1 hour)
Average speed = (80/3) * 2 miles/hour
Average speed = 160/3 miles/hour
Rounded to the nearest tenth, the average speed needed to drive the same distance in half an hour is approximately 53.3 miles per hour.