Town Y and Town Z were 512 km apart. Car A left Town Y for Town Z at a speed of 32km/h. An hour later car B left Town Z for Town Y at twice of car A ‘s speed. How long would it take for the two cars each other after car A left Town Y
distance = speed * time, so
32t + 2*32(t-1) = 512
now solve for t.
let the time taken until they meet be t hours
distance covered by car A = 32t
distance covered by car B = 64(t-1)
so
32t + 64(t-1) = 512
32t + 64t - 64 = 512
96t = 576
t = 6
draw your conclusion
To figure out how long it would take for the two cars to meet after car A left Town Y, we need to find out at what time car B leaves Town Z.
Car A left Town Y and traveled for an hour. So, by the time car B leaves Town Z, car A has already been traveling for 1 hour.
Now, let's calculate the distance car A covers in that 1 hour:
Distance = Speed x Time
Distance = 32 km/h * 1 hour
Distance = 32 km
This means that after 1 hour, car A has already traveled 32 km.
The distance between the two towns is 512 km, and car A has already traveled 32 km. So, the remaining distance that car A and car B need to cover to meet each other is:
Total Distance - Distance Covered by Car A
512 km - 32 km = 480 km
Now, we know that car B is traveling at twice the speed of car A. Therefore, the speed of car B is:
Speed of Car A * 2
32 km/h * 2 = 64 km/h
Next, we can calculate the time it would take for car B to cover the remaining distance of 480 km:
Time = Distance / Speed
Time = 480 km / 64 km/h
Time = 7.5 hours
So, it would take car B 7.5 hours to cover the remaining distance and meet car A.
To find the total time taken for the two cars to meet after car A left Town Y, we need to add the one hour that car A was already traveling:
Total Time = Time taken by Car B + Time car A was already traveling
Total Time = 7.5 hours + 1 hour
Total Time = 8.5 hours
Therefore, the two cars would meet each other after 8.5 hours from the time car A left Town Y.