Chapter 4.8, Problem 11P

To determine

To calculate: The distance boy biked.

Answer to Problem 11P

The total distance travelled by the boy is $22.50\text{km}$ .

Explanation of Solution

Given information:

The rate of ascent of bike is $3\text{km}/\text{h}$ less than the rate of descent.

Time taken by boy to go up: $2.5h$

Time taken by boy to go down: $1.5h$

Let the speed of boy down the hill be $x\text{km}/\text{h}$ .

The speed of boy up the hill be $(x-3)\text{km}/\text{h}$ .

Time taken by boy to go up: $2.5h$ .

Time taken by boy to go down: $1.5h$ .

As, $\text{Distance}=(\text{speed})(\text{time})$

Distance travelled while going downward $=1.5\times x=1.5x\text{km/h}$

Distance travelled while going upward $=2.5\times (x-3)=(2.5x-7.5)\text{km/h}$

Since, both distances are equal,

  $2.5x-7.5=1.5x$

  $x=7.5\text{km}/\text{h}$

Speed of the boy to go downhill will be $x=7.5\text{km}/\text{h}$ .

Speed of the boy to go uphill will be $x-3=7.5-3=4.5\text{km/h}$ .

Total distance travelled is:

  $(4.5)(2.5)+(7.5)(1.5)$

  $=11.25+11.25$

  $=22.50$

The total distance travelled by the boy is $22.50\text{km}$ .