Page 49 - Algebra

Explanation:
1. Let the still water speed of the boat be x km/hour The speed of the stream is y km/hour
Let the speed of the boat down the stream = x + y Speed of the boat upstream = x – y
20 + 15 =12 𝑥−𝑦 𝑥+𝑦
25 + 30 =17 𝑥−𝑦 𝑥+𝑦
Let 1 = p and 1 = q 𝑥−𝑦 𝑥+𝑦
20p + 15q = 12...........(1) 25p + 30q = 14............(2) Multiply (1) by 2
60p + 30q = 24
25p + 30q = 17
Subtract the two equations 35p = 7
p =1 5
1=1 𝑥−𝑦 5
5 = (x – y)
5 = x – y......................(3)
25p + 30q = 14 25 × 1 + 30q = 14
5
30q = 9 q= 9
q= 3 10
1=3
𝑥+𝑦 10
10 = 3x + 3y................(4) Multiply (3) by 3
15 = 3x – 3y
Add the above and (4) 25 = 6x
x = 25 km/hr 6
30
Page 48 of 177
Algebra I & II