Two hikers begin walking towards each other from an initial distance of 20 km
apart. Hiker P averages 4 km/h while hiker Q averages 6 km/h. When and where do
they meet?
d1 = distance hiker P traveled,
d2 = distance hiker Q traveled,
d1 + d2 = 20 km.
4t +6t = 20 km,
10t = 20,
t = 2 h = time they met.
4t = 4 * 2 = 8 km = d1.
6t = 6 * 2 = 12 km = d2.
To find out when and where the hikers meet, we need to determine how long it takes for them to meet and their meeting point.
Let's denote the time it takes for the hikers to meet as 't'. We can use the formula:
Distance = Speed × Time
For hiker P, the distance traveled is 4t km.
For hiker Q, the distance traveled is 6t km.
Since they are walking towards each other, the total distance they travel is equal to the initial distance between them, which is 20 km. Therefore, we have the equation:
4t + 6t = 20
Combining like terms, we get:
10t = 20
Dividing both sides by 10, we find:
t = 2
So, it takes 2 hours for the hikers to meet.
Now, let's find the meeting point. Since hiker P is traveling at 4 km/h and it takes 2 hours to meet, hiker P will have traveled 8 km (4 km/h × 2 h) from their starting point. Similarly, hiker Q will have traveled 12 km (6 km/h × 2 h) from their starting point.
To find the meeting point, we subtract the distance traveled by hiker P from the initial distance between them:
20 km - 8 km = 12 km
Therefore, the hikers will meet 12 km away from hiker P's starting point and 8 km away from hiker Q's starting point, after 2 hours of walking.