**Q8. A boat covers (x + 30) km downstream in 5 hours, and (y + 40) km upstream distance in 15 hours. Find the time taken by the boat to travel (4x + 2y) km downstream, if the speed of the boat in still water is thrice that of the stream (2 km/h). **

Solution:

Speed of the stream = 2 km/h

Speed of the boat in still water = 3 × 2 = 6 km/h

Downstream speed = Speed of the boat in still water + Speed of the stream Upstream speed = Speed of the boat in still water - Speed of the stream Downstream speed = 6 + 2 = 8 km/h

Upstream speed = 6 - 2 = 4 km/h

Downstream distance: (x + 30) km in 5 hours

Downstream speed = 8 km/h

Distance = Speed × Time

(x + 30) = 8 × 5

(x + 30) = 40

x = 40 - 30

x = 10

Upstream distance: (y + 40) km in 15 hours

Upstream speed = 4 km/h

Distance = Speed × Time

(y + 40) = 4 × 15

(y + 40) = 60

y = 60 - 40

y = 20

Time taken to travel (4x + 2y) km downstream: Downstream distance = 4x + 2y

Downstream distance = 4(10) + 2(20)

Downstream distance = 40 + 40

Downstream distance = 80 km

Time taken = Distance / Downstream speed

Time taken = 80 / 8

Time taken = 10 hours