Question

Jonathan increased his rate of walking by 25% at halfway to his destination and therefore arrived half an hour earlier than was planned. How long did it take for Jonathan walk to his destination?O

Answer 1

1.67 hours

Explanation:

Let the original speed of Jonathan =
`x` units/hr

Let the original time taken by Jonathan =
`y` hours

Let the distance =
`D` units

Formula for distance is given as:

`Distance = Speed * Time`

Given that half the distance is covered by original speed.

`\Rightarrow (D)/(2) = (x)/(2)* (y)/(2)\\\Rightarrow D = (xy)/(2) ..... (1)`

Half the distance is covered by increasing the rate by 25%.

i.e. increased speed:

`(5)/(4)x\ units/hr`

Hence, Time taken:

`(y)/(2)-(1)/(2)`

Distance traveled is half of the total distance:

`\Rightarrow (D)/(2) = (5x)/(4)* ((y)/(2)-(1)/(2))\\\Rightarrow D = (5x)/(2)* ((y)/(2)-(1)/(2)) .... (2)`

Dividing (1) by (2):

`(xy* 4)/(2* 5x(y-1)) = 1\\\Rightarrow 2y=5y-5\\\Rightarrow 3y=5\\\Rightarrow y =1.67\ hours`