# at 7:00am joe starts jogging at 6 mi/h. at 7:10 am ken starts after him. how fast must ken run to overtake joe at 7:30am?

If Joe runs at 6 mi/hr for 30 minutes (7:00 to 7:30), his distance traveled is 6 mi/hr x 0.5 hr = 3 miles.
Ken starts at 7:10 and runs until 7:30 for a time of 20 minutes. For Ken to just catch up with Joe in 20 minutes, the rate - distance/time = 3 mi divided by 1/3 Hr =3 x 3/1 = 9 miles/hr. So to overtake Joe, Ken must run one step faster somewhere in the 3 miles.

## To calculate the speed at which Ken must run in order to overtake Joe at 7:30 am, we first need to determine the distance that Ken needs to cover in the remaining time.

Since Joe has already covered 3 miles in 30 minutes, we know that his speed is 6 miles per hour. Therefore, in the remaining 20 minutes from 7:10 am to 7:30 am, Joe would have covered 6 miles per hour x (20 minutes / 60 minutes per hour) = 2 miles.

Given that Ken needs to cover the same 3 miles that Joe has already covered, plus an additional 2 miles that Joe would have covered during Ken's running time, Ken needs to cover a total distance of 3 miles + 2 miles = 5 miles.

To determine Ken's required speed, we can use the equation speed = distance / time. Ken needs to cover 5 miles in the remaining 20 minutes, so his required speed would be 5 miles / (20 minutes/60 minutes per hour) = 5 miles / (1/3 hour) = 15 miles per hour.

Therefore, Ken must run at a speed of 15 miles per hour in order to overtake Joe by 7:30 am.

## To calculate the speed at which Ken must run to overtake Joe at 7:30am, we need to determine the time it takes for Ken to cover the same distance as Joe and then find the average speed.

Joe runs for 30 minutes, covering a distance of 3 miles. Therefore, his speed is 3 miles / 0.5 hours = 6 miles per hour.

Ken starts running at 7:10am and has 20 minutes until 7:30am. To catch up with Joe in this time, Ken needs to cover the same distance of 3 miles.

Now, let's calculate Ken's required speed. We know that distance = speed x time. Rearranging the formula, we have speed = distance / time.

Ken's required speed = 3 miles / (20 minutes / 60 minutes per hour)
= 3 miles / (1/3 hours)
= 3 miles / (1/3)
= 3 x 3/1
= 9 miles per hour.

Therefore, Ken must run at a speed of 9 miles per hour to overtake Joe at 7:30am.