Two bike riders X and Y both start at 2 pm riding towards each other from 40 km apart.
X rides at 30 km/h, Y at 20 km/h. If they meet after t hours, find when and where they meet.
To find when and where the two bike riders meet, we can start by finding the time it takes for them to meet.
Let's assume t is the time (in hours) it takes for the riders to meet.
Since X is riding at a speed of 30 km/h and Y is riding at a speed of 20 km/h, their combined speed is 30 km/h + 20 km/h = 50 km/h.
We also know that the total distance between them is 40 km.
Using the formula: distance = speed × time, we can calculate the total distance traveled by both riders.
For X, the distance traveled is 30 km/h × t hours = 30t km.
For Y, the distance traveled is 20 km/h × t hours = 20t km.
Since they are moving towards each other, the sum of their distances traveled should be equal to the total distance between them:
30t km + 20t km = 40 km.
Simplifying the equation:
50t km = 40 km.
Dividing both sides of the equation by 50:
t = 40 km / 50 km/h = 0.8 hours.
Therefore, it takes 0.8 hours (or 48 minutes) for X and Y to meet.
To find where they meet, we can calculate the distance each rider has traveled at that time.
For X, the distance traveled would be 30 km/h × 0.8 hours = 24 km.
For Y, the distance traveled would be 20 km/h × 0.8 hours = 16 km.
Since they meet after 0.8 hours, X would have traveled 24 km and Y would have traveled 16 km. They meet at the point where their combined distances equal the total distance between them:
24 km + 16 km = 40 km.
Therefore, they meet at the 40 km mark, which is 24 km from the starting point of X and 16 km from the starting point of Y.
let the distance travelled by X be x km
then the distance travelled by Y has to be 40-x km
time taken by X = x/30
time taken by Y = (40-x)/20
but when they meet, they both took the same time, so
x/30 = (40-x)/20
take over ...