Chapter 5.3, Problem 34E

To determine

To find the speed of current

Answer to Problem 34E

Speed of current is $\frac{1}{12}$ miles/minute.

Explanation of Solution

Given information:

Time taken to travel downstream= 40 minutes

Time taken to travel upstream= 20 minutes

Distance= 20 miles

Calculation:

Let the speed of boat be x and speed of current be y .

Also,

  $speed=\frac{d}{t}$

Where $d$ is distance and $t$ is time

According to question,

On going downstream, the speed of current add, resulting into less time taken. So,

  $x+y=\frac{20}{40}$(1)

On going upstream, the speed of current subtracts, resulting into more time taken. So,

  $x-y=\frac{20}{60}$(2)

As the coefficients of y In (1) and (2) are same, add,

  $x+y+x-y=\frac{20}{40}+\frac{20}{60}$

Solving,

  $2x=\frac{60+40}{120}$

Hence, $x=\frac{5}{12}$

Put in (1),

  $\frac{5}{12}+y=\frac{20}{40}$

Solving,

  $y=\frac{20}{40}-\frac{5}{12}$

And

  $y=\frac{60-50}{120}$

Hence, speed of current is $\frac{1}{12}$ miles/minute.