Places A and B are 80km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8hours and if they towards each other they meet in 1 hour 20 minutes. Find the speed of cars.
Answers
Answer:
In this case, let us suppose that the speed of one car is A Km/hr
let us suppose that the speed of another car is B Km/hr
Now, when they move in the same direction, their net speed gets reduced and the net speed is equal to the subtraction of speed of slow car from the speed of fast car. The concept behind this is that if there are two cars moving in the same direction, one car has to move at more speed than the other car in order to overtake it. Now, in this case of overtaking, the car that overtakes has net speed estimated by reducing the speed of the slow car from the fast car.
In the same direction case, one car starting from Point A has to move 80 Km more than the X distance, the another car moves in the same time period. Let us suppose that they meet at some distance X.
So, in this case, we have the following expression.
Time of Car A = Time of Car B
(80 + X)/A = X/B = 480 min
80 + X = 480A
X = 480B
480A + 480 B = 80+X+X
480(A+B) = 80+2X
A+B = (80+2X)/480
When the two cars move in opposite direction, their net speed gets increased and the net speed is equal to the sum of the speed of both the cars.
In the opposite direction case, the total distance is 80 Km. So, one car starting from Point A has to move Y Km and the another car has to move 80-Y Km in the same time period. Let us suppose that they meet at some distance Y.
So, in this case, we have the following expression.
Time of Car A = Time of Car B
(Y)/A = (80-Y)/B = 80 min
Y = 80A
80-Y = 80B
80A + 80B = Y+80-Y
80(A+B) = 80
A+B = 1
Now from the above case and below case:
1 = (80+2X)/480
480 = 80 + 2X
2X = 400
X = 200
80 + 200 = 480A
A = 280/480
A = 7/12
A + B = 1
B = 1-A
B = 5/12
Y = 80A
Y = 80*7/12
Y = 140/3 Km
We can recheck our answer by putting values in the expresion, we derived earlier:
(80-Y)/B = 80
so we have Y = 140/3
B = 5/12
Now,
(80-(140/3))/(5/12)
= (240-140)/3 * 12/5
= 100/3 * 12/5
=100*4/5
=20*4
=80
Note that in this case we have supposed the speed to be in Km/min by converting the time into minutes. So, if you want the speed to be in Km/hr, convert it by multiplying the speed by a factor of 60 min.
Answer:
Speed of Car A and B are 35 km / hr and 25 km / hr respectively.
Step-by-step explanation:
Let the speed of car at A is x km / hr and at B is y km / hr
Case 1.
8 x - 8 y = 80
x - y = 10
x = 10 + y ... ( i )
Case 2.
4 / 3 x + 4 / 3 y = 80
x + y = 60
x = 60 - y ... ( ii )
From ( i ) and ( ii )
10 + y = 60 - y
y = 25
Putting value of y in ( i )
x = 10 + 25
x = 35 .