Question

Yashasvi rides a bicycle at a uniform speed if the speed had been 4km more it would be have taken 1hour less to travel 48 km distance determined her speed

Answer 1

Topic

Quadratic Equation

Given

Yashasvi rides a bicycle at a uniform speed. If the speed had been 4km/h more it would have taken 1 hour less to travel a distance of 48 km.

To find

Speed of bicycle rider.

Formula to be Used

Speed = $\frac{Distance}{Time}$

Time = $\frac{Distance}{Speed}$

Solution

Let her speed be 'x' and time taken be 't'.

x = $\frac{48}{t}$ km/hr

t = $\frac{48}{x}$hr

Now,

It is given that she would have taken 1 hour less, if her speed would have been 4 km/h more.

So,

New speed = ( x + 4 ) km/hr

New Time = ( t - 1 ) hr

Speed = Distance / Time

( x + 4 ) = $\frac{48}{t - 1}$

t - 1 = $\frac{48}{x+4}$

t = $\frac{48}{x+4}$ + 1

t = $\frac{48 + x + 4}{x+4}$hr

t = $\frac{52 + x}{x+4}$ hr

Now, equate both 't' obtained as they are equal.

$\frac{48}{x}$hr = $\frac{52 + x}{x+4}$ hr

Cross multiply,

( x ) × ( 52 + x ) = 48 × ( x + 4 )

52x + x² = 48x + 192

x² + 52x - 48x - 192 = 0

x² + 4x - 192 = 0

x² + 16x - 12x - 192 = 0

x( x + 16 ) - 12( x + 16 ) = 0

( x + 16 )( x - 12 ) = 0

So, either

x + 16 = 0

x = - 16 or

x - 12 = 0

x = 12

As we know, speed can't be negative. So, we will reject x = -16 and accept x = 12.

So, the speed of rider is 12 km/hr.

Answer

Speed of Yashasvi is 12 km/hr.