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Nataly [62]
3 years ago
13

A bus travels 300 kilometers at a given speed. If the speed is increased by 5 kilometers per hour, the trip will be reduced by t

wo hours. Find the speed.
Mathematics
1 answer:
Margaret [11]3 years ago
3 0

Answer:

25km/hr (take the word train as bus )

Step-by-step explanation:

Answer

Let x km/hr be the constant speed of the train,

Then Time taken to cover 300km=

x

300

hrs

Time taken to cover 300km when the speed is increased by 5km/hr=

x+5

300

hours

It is given that the time to cover 300km is reduced by 2 hours

∴

x

300

−

x+5

300

=2

⇒

x(x+5)

300(x+5)−300x

=2⇒2x

2

+10x=1500

⇒x

2

+5x−750=0⇒x

2

+30x−25x−750=0

⇒(x+30)(x−25)=0⇒x=25orx=−30

But x cannot be negative. Therefore x=25

Hence, the original speed of the train is 25km/hr

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Step-by-step explanation:

= 7 \frac{1}{2} .1 \frac{3}{5}

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6 0
2 years ago
The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rec
igomit [66]

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 m^{2}

From there

x * (2x - 4) = 70

2x^{2} - 4x = 70

2x^{2} - 4x - 70 = 0

x^{2} - 2x - 35 = 0

Now we have a quadratic equation, which is  ax^{2} + bx + c = 0, where a \neq 0

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Discriminant (D) formula is b² - 4ac

D = -2^{2}  - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are  \frac{- b - \sqrt{D}  }{2a} and \frac{- b + \sqrt{D}  }{2a}

x_{1} =  \frac{- (-2) - \sqrt{144} }{2} = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

x_{2} = \frac{- (-2) + \sqrt{144} }{2} = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)

8 0
3 years ago
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Firlakuza [10]

Answer:

x\geq -8

Step-by-step explanation:

-9x+8\leq 80

       -8      -8

₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋

\frac{-9x}{-9} \leq \frac{72}{-9}

     ⇵  

x\geq -8

7 0
3 years ago
Read 2 more answers
The Rawlins family has travelled 600 km on their vacation. This has taken them 8 hours. If they continued at the same rate, how
spin [16.1K]

Answer:

B. 28 hours

Step-by-step explanation:

GIVEN :- <em>Time taken by family to travel 600 km is 8 hours</em>

CALCULATIONS :-

<em>To calculate the time to travel 2100 km, we need to calculate distance traveled in 1 hour</em>

<em>Distance traveled in 1 hour = 600 km ÷ 8</em>

<em>                                              = 75 km</em>

<em>Time required to travel 2100 km = 2100 ÷ 75</em>

<em>                                                         = </em><em>28 hours</em>

Therefore time required to travel 2100 km is 28 hours.


6 0
4 years ago
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Elis [28]

Given:

To prove ∆LMN ≅ ∆PQR by SSS you need _____________ and

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The missing values.

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6 0
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