Town Y and town Z were 512km 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 to pass each other after Car A left Town Y?
Please check
Car A time = 512/32 = 16 hrs
Car B time= 512/64 = 8hrs
So they pass each other at 8 hours???
Not quite.
Make a sketch, let P be the point where they meet.
Let YP = x, then ZP = 512-x
the difference in their times is 1 hour, so ..
x/32 - (512-x)/64 = 1
2x - 512 + x = 64
3x = 576
x = 192
time = 192/32 hours or 6 hours
To determine the time it takes for the two cars to pass each other after Car A leaves Town Y, we need to calculate the time it takes for Car B to catch up to Car A.
Let's break down the problem step by step:
1. Car A's speed is 32 km/h. To determine the time it takes for Car A to reach Town Z, we divide the distance between the two towns (512 km) by Car A's speed: 512 km รท 32 km/h = 16 hours. Therefore, Car A takes 16 hours to reach Town Z.
2. Car B's speed is twice that of Car A's speed, so Car B's speed is 2 x 32 km/h = 64 km/h. Now, we need to find out how long it takes for Car B to catch up to Car A.
3. Since Car A has a head start of 1 hour, we subtract this hour from the time it took Car A to reach Town Z: 16 hours - 1 hour = 15 hours. Therefore, Car B takes 15 hours to catch up to Car A.
So, the two cars will pass each other 15 hours after Car A leaves Town Y, not 8 hours as previously calculated.
Please double-check your calculations.