Question

A man rows a boat at a speed of 15 mph in still water. Find the speed of the river if it takes her 4 hours 30 minutes to row a boat to a place 30 miles away and return.what is the answer?

Answer 1

Let the speed of the river = x mph

Speed of boat on outward journey = (15 – x) mph (Assuming the outward journey is upstream)

Speed on boat on return journey = (15 + x) mph

Time = Distance/Speed

4 hours 30 minutes = 4.5 hours

Total time taken = 30/(15 – x) + 30/(15 + x) = 4.5

       30(15 + x) + 30(15 - x)
     ___________________           = 4.5         
          (15 – x)(15 + x)

450 + 30x + 450 – 30x = 4.5(225 – x^2)


900 = 4.5(225 – x^2)


200 = 225 – x^2

x^2 = 25

x = 5

So, the speed of the river = 25 mph

Answer 2

Given, boat goes and returns. That is both upstream and downstream.

Boat Speed (s) = 15

Let river speed = x

Upstream speed = 15-x

Downstream speed = 15+x

Given time = 9/2 (ie. 4hr 30min is 9/2 hrs)

Distance = 30

Formula: speed = distance/ time

- Time = distance/ speed

Time = upstream speed + downstream speed

9/2 = (30/15+x) + (30/15-x)

9/2 = 2*450/ 15^2-x^2

15^2-x^2 = 200

x^2 = 225-200

x^2 = 25

x = 5