1.  $\frac{x+y}{2}$= 7 , x + y = 14

y = 14-x, and xy = 45

x(14 – x) = 45 whose solution gives x = 5 or x = 9. Thus, the scores are 5 and 9.

Answer D

2. Let the speed of the current be c km/hr.

The speed of the boat going downstream (with the current) is:

15 + c km/hr

The speed of the boat going upstream (against the current) is:

15 – c km/hr

Time Calculation

Time taken to travel downstream (with the current) = 63/15 + c

Time taken to travel upstream (against the current) = 63/15 – c

According to the problem, the time taken to travel upstream is 4 hours more than the time taken to travel downstream:

63/15 – c = 63/15 + c + 4

Multiply through by (15 – c)(15 + c) to eliminate the denominators:

63(15 + c) = 63(15 – c) + 4(15 – c)(15 + c)

945 + 63c = 945 – 63c + 4(225 – c^2)

945 + 63c = 945 – 63c + 900 – 4c^2

Combine like terms:

63c + 63c + 4c^2 = 900

4c^2 + 126c – 900 = 0

Solving the quadratic equation

2c^2 + 63c – 450 = 0

c = -63 ± 87/4

Calculating both potential solutions:

c = 24/4 = 6

c = -150/4 = -37.5 (not valid since speed cannot be negative)

Thus, the speed of the current is:

6 km/hr

Answer B