Two cars leave simultaneously from points A and B, the distance between which is 280km. If the cars move to meet each other, they’ll meet in 2 hours. But if they move in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours. What is the speed of each of the cars?

bararskzs

bararskzs

Answered question

2022-12-22

Two cars leave simultaneously from points A and B, the distance between which is 280km. If the cars move to meet each other, they’ll meet in 2 hours. But if they move in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours. What is the speed of each of the cars?

Answer & Explanation

wiskixk8

wiskixk8

Beginner2022-12-23Added 5 answers

Explanation:
Given:
When two vehicles simultaneously depart from locations A and B, their distance from one another is 280km
At certain point the cars move to meet each other in 2 hours.
Also, When they move in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours.
To find:
The speed of each of the cars.
Explanation:
Speed is defined as, “the ratio of the distance traveled by the time taken”.
That is, Speed=distancetraveledtimetaken
Let x be the speed of the car at point A, and y be the speed of the car at point B.
Also d1 be the distance of the car from point A and d2 be the distance of the car from point B.
From the car at point A and the given condition, if the cars move to meet each other in 2 hours, t=2.
The speed of the car from point A is,
x=d12d1=2x
Similarly, the speed of the car from point A is,
y=d22d2=2y
If the distance between both cars is 280km, then we get
d1+d2=2802x+2y=280x+y=140
Additionally, if they proceed in the same direction, the vehicle departing from point A will catch up with the car going from point B in 14 hours. we get
x=d114d1=14x
And,
y=d214d2=14y
So,
d1=d2+28014x=14y+28014x-14y=280x-y=20................(2)
Now add both sides of the equation (1) and equation (2).
x+y+x-y=140+202x-0y=1602x=160x=1602x=80
Substitute the obtained value of x in equation (2) to find the value of y.
80-y=20y=80-20y=60
Therefore, the value of x is 80, and the value of y is 60.
Hence, the speed of the car from point A is 80kmh and the speed of the car from point B is 60kmh

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