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Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and If they move in the opposite directions, they meet 1 hour and 20 minutes. Find the speeds of the cars.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The speed of car A is 35 km/hr and of car, B is 25 km/hr. Let the speed of the vehicle leaving from point A be x km/hr and the vehicle leaving from point B be y km/hr.
Given that the total distance = is 80 km
Also it is given that 1 hour 20 mins = 1 + 20/60 hours = 1 + ⅓ hours = 4/3 hour
According to the question we have, In 8 hours, a car travelling in the same direction will encounter another.
Therefore,
Distance travelled from B = 8y km
Because we know that Distance = Speed x Time
Distance travelled from A = 8x
Now, according to the given condition the equation formed is:
8x – 8y = 80 because the difference between the two automobiles’ total distances = is 80km
The above equation becomes:
x – y = 10 ….(i)
The same is true for cars travelling in the opposite direction; they will collide in one hour and 20 minutes.
Distance travelled from B = 4y/3
Distance travelled from A = 4x/3
By adding them we get the total distance travelled or covered:
The total distance travelled = 4x/3 + 4y/3
According to the question, we can form the equation:
80 = 4x/3 + 4y/3
In simplification we get:
240 = 4x + 4y
60 = x + y …. (ii)
Equation (i) and Equation (ii) are added together to give us:
x + y + x – y = 60 + 10
x = 35
When we change the value of x in (ii), we obtain
60 = 35 + y
y = 60 – 35 = 25
Thus, the speed of the car as it leaves point A is 35 km/hr. An automobile leaves point B moving at a speed of 25 km/hr.
Summary:
Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and If they move in the opposite directions, they meet 1 hour and 20 minutes. Find the speeds of the cars.
Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and If they move in the opposite directions, they meet 1 hour and 20 minutes. The speed of car A is 35 km/hr and car B is 25 km/hr.