Ben can run six miles in forty-eight minutes. If Luke can run twenty percent faster than Ben, how many minutes will Luke take to run nine miles?
Please provide COMPLETE solutions with explanation please
Ben's speed is 6mi/48min = 1/8 mi/min
Luke's speed is 6/5 * 1/8 = 3/20 mi/min
9mi/(3/20 mi/min) = 9*20/3 = 60 min
or, Ben's speed is 60/8 = 15/2 mi/hr
Luke's speed is 6/5 * 15/2 = 9 mi/hr
To find out how many minutes Luke will take to run nine miles, we need to first determine his running speed in miles per minute.
Given that Ben can run six miles in forty-eight minutes, we can calculate his running speed as follows:
Running speed of Ben = Distance / Time
= 6 miles / 48 minutes
= 0.125 miles per minute
Since Luke runs twenty percent faster than Ben, we can calculate his running speed by increasing Ben's speed by twenty percent:
Increase in speed = 0.125 miles per minute * 20% = 0.125 * 0.20 = 0.025 miles per minute
Luke's running speed = Ben's running speed + Increase in speed
= 0.125 miles per minute + 0.025 miles per minute
= 0.150 miles per minute
Now, we can use Luke's running speed to calculate the time it will take him to run nine miles:
Time taken by Luke = Distance / Running speed
= 9 miles / 0.150 miles per minute
= 60 minutes
Therefore, Luke will take sixty minutes to run nine miles.