Question

While cycling along the wind a boy can cover a distance of 30 km in 3 hours and for returning for the same distance he takes 5 hours. Find the speed of wind and speed of cycling in still air

Answer 1

Solutions :-

Let the speed of cycling in still air be x
And the speed of wind be y

We know that,
Time = Distance / Speed

According to the question,
30/(x + y) = 3
=> [ 3x + 3y = 30] × 5 _____(i)
30/(x - y) = 5
=> [ 5x - 5y = 30] × 3 _____(ii)


Subtract the equation (ii) from equation (i). we get,

(15x + 15y) - (15x - 15y) = 150 - 90
=> 30y = 60
=> y = 60/30 = 2


Putting the value of y in equation (i) we get,

3x + 3 × 2 = 30
=> 3x + 6 = 30
=> 3x = 30 - 6
=> 3x = 24
=> x = 24/3 = 8



Hence,
The speed of cycling in still air = 8 km/hr
And the speed of wind = 2 km/hr

Answer 2

$<b>$
Solution:-

Let the speed of Cycling be x km/hr.

& The speed of Wind be y km/hr.

Distance 1 = 30 km

Time = 3 hr.

$= > \frac{30}{x + y} = 3 \\ \\ = > 30 = 3x + 3y \\ \\ = > 10 = x + y...........(1)$

&

Speed of Cycle when returning back :-

$= > \frac{30}{x - y} = 5 \\ \\ = > 30 = 5x - 5y \\ \\ = > 6 = x - y \\ \\ = > x = 6 + y.................(2)$

Putting x = 6 + y in eq 1. we get,

10 = x + y

=> 10 = 6 + y + y

=> 2y = 4

=>$\boxed{ y = 2 km/hr}$

Now, Putting y=2 in eq (2). we get,

x = 6 + y

=> $\boxed{x = 8 km/hr.}$

Hence

$\boxed{The Speed of Cycling in Still Air = x km/hr = 8 km/ hr.}$

& $\boxed{Speed of Wind = y km/hr = 2 km/hr}$