Mathematics, 30.10.2020 14:00 maddie306

The distance between two places is 200 km.; the time taken by motor car from one place to another is less by 2 hrs than the time taken by a zeep car. If the speed of the motor car is 5 km/hr. more than the speed of the zeep car, then by calculating let us write the speed of the motor car

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Answer from: alimfelipe

Given:

Distance between two places = 200 km

Motor car takes 2 hrs less than the zeep car to travel 200 km

Find:

the speed of the motor car

Solution:

Let the speed of the zeep car be x km/h.

Speed of motor car is 5 km/h more than speed of the zeep car.

→ speed of motor car = (x + 5) km/h.

Also,

Motor car takes 2 hrs less than the zeep car to travel 200 km.

Let the time taken by the zeep car be y hrs.

→ Time taken by motor car = (y - 2) hrs.

We know,

Distance = speed * time.

Hence,

For motor car:

→ 200 = (x + 5) * (y - 2) -- equation (1)

For zeep car:

→ 200 = xy

→ 200/x = y -- equation (2)

Substitute the value of y in equation (1).

→ 200 = (x + 5) * (200/x - 2)

→ 200 = x * (200/x - 2) + 5(200/x - 2)

→ 200 = 200 - 2x + (1000/x) - 10

→ 200 - 200 + 10 = 1000/x - 2x

→ 10 = (1000 - 2x²)/x

→ 10x = 1000 - 2x²

→ 2x² + 10x - 1000 = 0

→ x² + 5x - 500 = 0

→ x² + 25x - 20x - 500 = 0

→ x(x + 25) - 20(x + 25) = 0

→ (x - 20)(x + 25) = 0

• x - 20 = 0

→ x = 20

• x + 25 = 0

→ x = - 25

Speed cannot be negative. So , positive value is taken.

Hence,

Speed of zeep car = x = 20 km/h

speed of motor car = x + 5 = 20 + 5 = 25 km/h.

Now,

Substitute the value of x in equation (2).

→ 200/20 = y

→ 10 = y

Hence,

Time taken by zeep car = y = 10 hours.

Time taken by motor car = y - 2 = 10 - 2 = 8 hours.

Therefore, the speed of motor car is 25 km/h

I hope it will help you.

Regards.

Answer from: dacey4164

→ 200 = (x + 5) * (200/x - 2)

→ 200 = x * (200/x - 2) + 5(200/x - 2)

→ 200 = 200 - 2x + (1000/x) - 10

→ 200 - 200 + 10 = 1000/x - 2x

→ 10 = (1000 - 2x²)/x

→ 10x = 1000 - 2x²

→ 2x² + 10x - 1000 = 0

→ x² + 5x - 500 = 0

→ x² + 25x - 20x - 500 = 0

→ x(x + 25) - 20(x + 25) = 0

→ (x - 20)(x + 25) = 0

• x - 20 = 0

→ x = 20

• x + 25 = 0

→ x = - 25

so the answer is 20

Step-by-step explanation:

Answer from: Quest

Y=-2x-6 is the answer

Answer from: Quest

so, converting firstly the mixed fractions to improper fractions and then "adding".

$\bf \stackrel{mixed}{2\frac{9}{10}}\implies \cfrac{2\cdot 10+9}{10}\implies \stackrel{improper}{\cfrac{29}{10}}~\hfill \stackrel{mixed}{5\frac{4}{15}}\implies \cfrac{5\cdot 15+4}{15}\implies \stackrel{improper}{\cfrac{79}{15}} [-0.35em] ~\dotfill$

$\bf -\cfrac{29}{10}+\left( -\cfrac{79}{15} \right)\implies -\cfrac{29}{10}-\cfrac{79}{15}\implies \stackrel{\textit{using the lcd of 30}}{\cfrac{-(3)29-(2)79}{30}}\implies \cfrac{-87-158}{30} \cfrac{-245}{30}\implies -\cfrac{49}{6}\implies -8\frac{1}{6}$

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The distance between two places is 200 km.; the time taken by motor car from one place to another is...