Answer to Question #165341 in Math for Alex

Question

Peter travels from his place to his uncle house a distance of 30km.He cycles for two thirds of the journey before walking for the rest of the journey. If his cycling speed is 10km/hr more than the walking speed and the whole journey took him 3hrs 20 minutes, calculate his cycling speed.

Answer 1

$3\ hr\ 20\ min=\dfrac{10}{3}\ hr$

Let $x$ km/hr be his walking speed. Then his cycling speed is $(x+10)$ km/hr.

$$\dfrac{\dfrac{2}{3}\cdot30}{x+20}+\dfrac{\dfrac{1}{3}\cdot30}{x}=\dfrac{10}{3}$$

$$6x+3(x+10)=x(x+10)$$

$$x^2+x-30=0$$

$$(x+6)(x-5)=0$$

$x_1=-6, x_2=5$

Since $x>0,$ we take $x=5.$

Then

$$x+10=5+10=15$$

His cycling speed is 15 km/hr.