Question

A motorboat takes a total of 10 hours to cover 120 km upstream and return. If it takes 15 hours to
cover 150 km downstream and 200 km upstream, find the speed of the motorboat in still water and
the speed of the stream

Answer 1

Answer:

25 km/hr and 5 km/hr

Step-by-step explanation:

Speed of motorboat- s

Speed of current- c

Equations based on given:

1. 120/(s+c)+120/(s-c)=10
2. 150/(s+c)+200(s-c)=15

Equation 1  simplified

• 120/(s+c)+120/(s-c)=10
• s^2-c^2=12(s-c+s+c)
• s^2-c^2=24s  

Equation 2 simplified

• 150/(s+c)+200/(s-c)=15
• 3(s^2-c^2)=30(s-c)+40(s+c)
• 3(s^2-c^2)=70s+10c
• 3(s^2-c^2)=72s

Equations compared:

• 72s=70s+10c
• s=5c

Final bit, one variable excluded:

• s^2-c^2=24s
• 25c^2-c^2=24*5s
• 24c^2-120c=0
• 24c(c-5) =0
• c=5
• s=25

Answer is 25 km/hr and 5 km/hr

Answer 2

Answer:

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr