Nicholas takes a boat ride down a river to visit an island a

Nicholas takes a boat ride down a river to visit an island at the mouth of the river. The boat leaves the docks at 9:15 a.m. and reaches the island at 10:34 a.m. He spends several hours on the island, and leaves on the return boat at 5:45. Because the boat is moving upriver against the current, the return trip takes 67 minutes longer than the trip to the island. Let v be the cruising speed of the boat.

Solution

f the speed of a boat in still water is v km/hr and the speed of the stream is c km/hr, then:

Speed downstream = (v + c) km/hr.----to the island

Speed upstream = (v - c) km/hr.----from the island

jpurney to the island took 79 min.

jpurney from the island took (79 +67) min = 146 min.

distance = d

a) v-c <=0

This means speed of stream is more than speed of boat in still water

which cannot be true amd v-c<=0 is not true

b) So, (v +c)*79 = (v-c)146

79v +79c = 146v -146c

225c = 67v ----> v/c = 225/67 .

So, option b is true

c) Now d/(v-c) -d/(v+c) =67

d[ ( v+c) - (v-c)]/(v^2 -c^2) =67

d[2c/(v^2 -c^2) ] = 67

dc/(v^2 -c^2 = 67/2

So, Option c is true.

d) d/(v+c) = 79 ---- (1)

d= 79v +79c

(d-79v)/79 =c

d/(v-c) = 146 ---- (2)

d= 146v -146c

146c = (146v -d)

c = (146v -d)/146

Equation both eqautions for c:

(d-79v)/79 = (146v -d)/146

(d -79v)/(146v -d) = 79/146

(d-79v)/(d-146v) = -79/146

which does not mtach with the given option

Hence not true