A jogger leaves home and runs at a constant speed of 4 miles per hour. Nine minutes later, a bicyclist follows along the same route at a constant speed of 15 miles per hour. Find the bicyclist's travel time needed to catch the jogger.
9 minutes = .15 hour
they both went the same distance.
bikers time ---- t hrs
jogger's time -- t+.15
15t = 4(t+.15)
15t = 4t + .6
11t = .6
t = .0545 hrs or 3.2727 minutes or 3 min and 16.4 seconds
3/11 minutes
Junior drove 55.6 miles then he drove 42 1/5 miles. How many miles did he drove in all??
To find the bicyclist's travel time needed to catch the jogger, we need to determine the distance the jogger travels in the 9 minutes between when the jogger starts and when the bicyclist starts.
The jogger runs at a constant speed of 4 miles per hour, which means in 1 minute, the jogger covers 4/60 = 1/15 miles.
Therefore, in 9 minutes, the jogger will have covered 9 * (1/15) = 9/15 = 3/5 miles.
Now, the bicyclist starts from home and needs to catch up to the jogger, who is 3/5 miles ahead.
The bicyclist travels at a constant speed of 15 miles per hour, so in 1 minute, the bicyclist covers 15/60 = 1/4 miles.
Therefore, to catch up to the jogger who is 3/5 miles ahead, the bicyclist needs to cover a distance of 3/5 miles.
The time it takes for the bicyclist to cover a distance of 3/5 miles at a speed of 15 miles per hour is:
Time = Distance / Speed = (3/5) / 15 = (3/5) * (1/15) = 1/25 hour = 60/25 minutes = 2.4 minutes.
So, the bicyclist's travel time needed to catch the jogger is 2.4 minutes.