Mathematics
Grade10
Easy

Question

A boat travels 8 miles upstream in the same amount of time it can travel 12 miles downstream. In still water the speed of the boat is 5 mi/h. What is the speed of the current?

  1. 1 mi/h
  2. 2 mi/h
  3. 0.5 mi/h
  4. 3.5 mi/h

hintHint:

We know that to travel upstream total speed would be speed of boat - speed of current and to travel downstream total speed would be speed of boat +speed of stream. Also, time taken both ways are same So, to find the speed of current we can find time taken both ways in each case and then equate them.

The correct answer is: 1 mi/h


    Let C be the speed of current.
    Upstream speed = 5 - C           Downstream speed = 5 + C
    s equals d over trightwards double arrow t equals d over s
    Time taken to travel 8 miles upstream = time taken to travel 12 miles downstream
    fraction numerator 8 over denominator 5 minus C end fraction equals fraction numerator 12 over denominator 5 plus c end fraction
    rightwards double arrow 8 left parenthesis 5 plus C right parenthesis equals 12 left parenthesis 5 minus c right parenthesis
    rightwards double arrow    40 plus 8 C equals 60 minus 12 C
    rightwards double arrow 20 c equals 20
    rightwards double arrow    C equals 1 mi divided by straight h

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