Pls Solve this motion Problem???

Question

Two boats started at the same point and rowed in opposite directions in still water. After 20 mins., the boats were 9 km apart. If one boat is 1 kph faster than the other boat, find the rate of each boat.

Answer 1

Let the speeds be 'x' and 'x+1' km/hr of the 2 boats.
20 min = (1/3) hour

Distance covered by first boat = speed* time = x/3 km

Distance covered by first boat = speed* time = (x+1)/3 km

Total distance covered by both = x/3 + (x+1)/3 = (2x+1)/3 km

Since they are 9 km apart after 20 mins:

(2x+1)/3 = 9

2x+1 = 27

2x = 26

x = 13

x+1 = 14

13 km/hr and 14 km/hr respectively are the rate/speeds of the boats.

Answer 2

Let the speed os the boat be x and x+1 kmph.
Distance travelled by them in 20 minutes or 1/3 hour=9 km
By the problem=1/3(x+x+1)=9
=>1/3(2x+1)=9
=>2x+1=27
=> 2x=26
=>x=26/2=13
Therefore,the speeds of the boat are 13 km and 14 km respectively

Answer 3

well, this is as close as I'll ge this early in the morning after work:)

ok...so after 20 mins, they were 9 km apart. so after an hour, they would be 27 km apart. The total rate of speed for the two boats is 27 km/hour. Since one boat is 1 km faster than the other, I just figured one is 14 km/hr and the second is 13 km/hr.
To check it, just take 1/3 of 14 km plus 1/3 of 13 km, and that should come real close to 9 km (showing the first 20 minutes of rowing).

Answer 4

Fitz has given the elegant and simple answer.

If v is one's speed, the other one's speed is v+1.

Since they are moving oppositely, the reative velocity of the second one with respect to the first one is 2v + 1.

2v + 1 = distance / time = 9/ (1/3) km /hour = 27.

v = 13km/h and v +1 = 14km/h.

Answer 5

After 1/3 of an hour (20 mins)- 9km apart
After 1 hour - 27 km apart

Speeds !4kph and 13kph