A boat travels 35 km upstream and then back again in 4 h 48 min. If the speed of boat in still water is 15km/h, what is the speed of the current.

Question

d = r x t 

Answer 1

As the total time is 4hrs and 48 minutes, or 4.8 hrs

 

Time travelling upstream + Time travelling downstream = 4.8

 

Solving D = R x T for T gets

T = D/R

 

The distance both ways is 35 km

 

Upstream the boat travels slower than in still water because of the current pushing on it. Let C be used for the speed of the current. The speed upstream can be found by taking the speed of the boat in still water and subtracting the speed of the current getting 15 - C

Downstream the speed of the boat can be found by adding the speed of the boat in still water and the speed of the current getting 15 + C

 

Therefore, using T = D/R the time travelled upstream can be expressed by 35/(15 - C)

The time downstream is 35/(15 + C)

 

Adding these two together and setting it equal to the total time gets

 

35/(15 - C) + 35/(15 + C) = 4.8

 

To solve this rational equatiion, multiply both sides by the common denominator of (15 - C)(15 + C) to get

 

35(15 + C) + 35(15 - C) = 4.8(15 + C)(15 - C)

 

Simplifying this gets

 

525 + 35C + 525 - 35C = 4.8(225 - C²)

1050 = 1080 - 4.8C²

 

Solving for C you will find the speed of the current to be 2.5 km/hr