Question

went to the picnic.
34. A bus covers a distance of 240 km at a uniform speed. Due to heavy rain, its speed gets reduced
by 10 km/h and as such it takes two hours longer to cover the total distance. Assuming the
uniform speed to be x km/h, form an equation and solve it to evaluate x.
(2016)
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Problems on Quadratic Equations
65​

Answer 1

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Gívèn :-

• A bus covers a distance of 240 km at a uniform speed, D = 240 km
• its speed gets reduced by 10 km/h
• It takes two hours longer to cover the total distance
• Uniform speed = x km/hr

To find :-

• The value of x by forming quadratic equations.

Solution :-

We have been given in the question, to assume the uniform speed of the bus x km/hr.

•°• Let the speed of the bus be x km/hr

As per the first condition,

• Its speed gets reducedby 10 km/h due to rain.

•°• Now, the speed of the bus will be the difference of the uniform speed and reduction of speed i.e 10 km /hr

•°• New Speed = x - 10 km/hr

As per the second condition,

• Bus takes two hours longer to cover the total distance.

Time = 2 hrs

Also mentioned in the question, the bus covers a distance of 240 km.

•°• Distance = 240 km

Time = 2 hrs

Speed = x - 10 km/hr

So now using the formula for time.

Time = $\bf\large\frac{distance}{speed}$

•°• Time taken to cover 240 km with speed of x km/hr = $\bf\large\frac{240}{x}$

Time taken to cover 240 km with a speed of x - 10 km/hr = $\bf\large\frac{240}{x-10}$

Get the two equations in linear state and solve them,

$\bf\large\frac{240}{x- 10}$ - $\bf\large\frac{240}{x}$ = 2

$\bf\large\frac{(240)(x) - 240(x-10)}{ x (x-10)}$ = 2

$\bf\large\frac{240x - 240x + 2400}{x^2 - 10x}$ = 2

$\bf\large\frac{2400}{x^2 - 10x}$ = 2

Cross multiplying,

2400 = 2 ( x² - 10x)

2400 = 2x² - 20x

2x² - 20x = 2400

2x² - 20x - 2400 = 0

÷ by 2

x² - 10x - 1200 = 0

Factors of 1200,

40 × 30 = 1200

- 40 + 30 = 10

x² - 40x + 30x - 1200 = 0

x ( x - 40) +30 ( x - 40) = 0

( x - 40) ( x + 30) = 0

x - 40 = 0 OR x + 30 = 0

x = 40 OR x = - 30

x = - 30 cannot be accepted, since speed cannot be negative.

Hence x = 40 is accepted.

•°• Value of x = 40 km/hr

Uniform speed of the bus = 40 km/hr