A motorboat takes 3 hours to travel 108 kilometers going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? Rate of the boat in still water:
Rate of the current:

45; 9

Step-by-step explanation:

1) if the rate of the boat in still water is 'b' and the rate of the current is 'c', then it is possible to write the rate of the boat going upstream: b-c, downstream: b+c.

2) the basic formula is: D=r*t, where D - distance, r - rate/velocity, t - time;

3) according to the condition it takes 3 hours to travel 108 km upstream, it means according to  the formula above 3(b-c)=108;

4) according to the condition it takes 2 hours to travel 108 km downstream, it means according to the formula above 2(b+c)=108;

5) if to make up the system of two equations, then:

6) rate of the boat in still water: 45 km/h;

rate of the current: 9 km/h.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for