A boat towing a water skier leaves a dock and travels east at a speed of 20mph. Two minutes later, a second boat towing another skier leaves the dock in the same direction at a speed of 25mph. How long will it take the second boat to overtake the first boat?
PLEASE help!? /:
first boat goes for t + 2 min at 20/60
second boat goes for t min at 25/60
distance = same = speed * time
20(t+2)/60 = 25 t/60
4(t+2) = 5 t
8 minutes = t
Thanks!! :)
distance = speed * time
the second boat travels 2 min less than the first boat
converting mph to miles/min, both boats traveled for m minutes, making the same distance.
m * 20/60 = (m-2) * 25/60
20m = 25m - 50
5m = 50
m = 10
10 min at 20mph = 20 * 10/60 = 200/60mi
8 min at 25mph = 25 * 8/60 = 200/60 mi
djegerdajuiopruteig
To find out how long it will take the second boat to overtake the first boat, we need to determine the distance between the two boats when the second boat starts.
First, let's convert the two-minute delay for the second boat into hours. There are 60 minutes in an hour, so two minutes is equal to two divided by 60 hours, which is 1/30 of an hour.
Since the first boat has been traveling for two minutes before the second boat starts, it will have covered a distance of (20 mph) x (1/30 hour) = 2/3 mile when the second boat starts.
Now that we know the distance between the two boats when the second boat starts, we can calculate how long it will take the second boat to catch up with the first boat.
Let's assume that it takes the second boat "t" hours to catch up with the first boat. In that time, the first boat will have traveled a distance of (20 mph) x "t" hours, and the second boat will have traveled a distance of (25 mph) x "t" hours.
Since the second boat is catching up with the first boat, the distance between them decreases. Therefore, we can set up the following equation:
(20 mph) x "t" hours - (2/3 mile) = (25 mph) x "t" hours
Simplifying the equation, we get:
5 mph x "t" hours = (2/3 mile)
To solve for "t", divide both sides of the equation by 5 mph:
"t" hours = (2/3 mile) / (5 mph)
Now we can calculate the time it will take for the second boat to overtake the first boat:
"t" hours = (2/3) / 5 = (2/3) x (1/5) = 2/15 hour
Converting this into minutes, we get:
"t" minutes = (2/15) x 60 = 8 minutes
Therefore, it will take the second boat 8 minutes to overtake the first boat.