Question

Places A and B are 100 km apart on a highway. One car starts from A and another
from B at the same time. If the cars travel in the same direction at different speeds,
they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What
are the speeds of the two cars?​

Answer 1

Answer:

40 km/hr and 60 km/hr

Step-by-step explanation:

let car which is presently at be called Car A and the other be called Car B

let the speed of car A be x km/hr

and the speed of car B be y km/hr

distance between A and B is 100 km

Case 1 : cars travelling towards each other

time taken = 1 hr

distance traveled by car A = x km

distance traveled by car B = y km

since they meet somewhere in between A and B

$x + y = 100 ...(1)$

Case 2 : cars travelling in same direction

time taken to meet = 5 hr

now when both the cars move in same direction one of the car will have greater speed.

when both these cars meet the car with greater speed will have covered a distance 100 km more than the car with lesser speed

let us assume that car B has lesser speed

and the car A is moving towards place B while car B is moving away from that place

distance traveled by car A = 5x km

distance traveled by car B = 5y km

Also we know that

$5x = 5y + 100\\which \ can \ be \ written \ as\\x = y+20\\x-y=20 ....(2)$

Adding equation 1 and 2

$2x = 120\\x =60\\from \ eq(1)\\x + y=100\\60+y=100\\y=40$

therefore car A travels with a speed of 60 km/hr

and car B with the speed of 40 km/hr

if we would have assumed that car A has lesser speed we would have got that car A travels with 40 km/hr and car B with the speed of 60 km/hr.Also in this case the car B would be travelling towards place A and car A away from that place

therefore the speed of the cars are 40 km/hr and 60 km/hr

Answer 2

Answer Distance between point A and B is 100 km

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the cars

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr.

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hr

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)x + y = 100 ....................(2)

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)x + y = 100 ....................(2)Add equation (1) and (2),

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)x + y = 100 ....................(2)Add equation (1) and (2),2x = 120

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)x + y = 100 ....................(2)Add equation (1) and (2),2x = 120x = 60

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)x + y = 100 ....................(2)Add equation (1) and (2),2x = 120x = 60put this value in equation (2),

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)x + y = 100 ....................(2)Add equation (1) and (2),2x = 120x = 60put this value in equation (2),60 + y = 100

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)x + y = 100 ....................(2)Add equation (1) and (2),2x = 120x = 60put this value in equation (2),60 + y = 100y = 40

between point A and B is 100 kmlet car starting from point A is Car A and Car starting from point B is Car B.To find: Speeds of the carslet Speed of Car A is x km/hr. Speed of Car B is y km/hrAccording to the question, (using speed, distance, time formula)5x - 5y = 100x - y = 20 .......................(1)x + y = 100 ....................(2)Add equation (1) and (2),2x = 120x = 60put this value in equation (2),60 + y = 100y = 40Therefore, Speed of the cars are 60 km/hr and 40 km/hr.