Question

A bus cover a distance of 90 km at a uniform speed had the seed been 15 km/hr more it would have taken 30 minutes less for the journey .Find the original speed of the bus ​

Answer 1

Correct Question:-

A bus covers a distance of 90 km at a uniform speed. Had the speed been 15km/hour more it would have taken 30 minutes less for the journey. Find the original speed of the bus.

Given:

• A bus covers a distance of 90 km at a uniform speed

• If the speed had been 15km/h more, it would have taken 30 minutes less for the journey.

To Find:

Original speed of bus

Solution:

Let the original speed be 'x' km/h

Time taken by bus to travel: 90/x km/h

New Speed =(x+15)km/h

$\sf{Time\:taken\:to\:travel={\dfrac{90}{x+15}}h}$

$\sf{\therefore{\dfrac{90}{x}}={\dfrac{90}{x+15}}={\dfrac{1}{2}}}$

$\sf{\implies}{90 \bigg({\dfrac{1}{x}}-{\dfrac{1}{x+15}}\bigg) = {\dfrac{1}{2}}}$

$\sf{{\implies}{\dfrac{x+15-x}{x(x+15)}}={\dfrac{1}{180}}}$

$\sf{\implies}{15 \times 180=x(x+15)}$

${\implies}\sf{2700=x^2 +15x}$

${\implies}\sf{x^2 +15x-2700}$

${\implies}\sf{x^2+60x-45x-2700}$

${\implies}\sf{x(x+60)-45(x+60)=0}$

${\implies}\sf{(x+60)(x-45)=0}$

Speed can not be negative.

∴Original speed of Bus=45km/h