Three friends anil, bala and chetan, from X to town X to town Y which was 4o km. Anil who had a bike started along with bala while chetan started simultaneously on foot. After some time , anil dropped bala on the way and went back to pick up chetan while bala proceeded to Y on foot. Anil picked up chetan and reached Y at the same time as bala. Anil traveled at 50km/hr. The speed at which bala and chetan walked was 10 km /hr . find the time after which anil turned back?
Break the total time into three periods:
x: when a&b are on the bike
y: when a rides back for c
z: when a&c are on the bike
since distance = time*speed, write the net distances traveled by each person:
a: 50x-50y+50z = 40
b: 50x+10y+10z = 40
c: 10x+10y+50z = 40
Now solve for x, the time when a turned back.
To find the time after which Anil turned back, let's break down the steps of their journey:
1. The distance between town X and town Y is 40 km.
2. Anil and Bala started together from town X, with Anil on his bike.
3. Chetan started simultaneously on foot.
4. After some time, Anil dropped Bala on the way and went back to pick up Chetan.
5. Bala continued on foot towards town Y.
6. Anil picked up Chetan and reached town Y at the same time as Bala.
Let's assume that Anil traveled for 't' hours before turning back to pick up Chetan.
During this time:
1. Anil traveled for 't' hours at a speed of 50 km/hr, covering a distance of 50t km.
2. Bala traveled at a speed of 10 km/hr for the same 't' hours, covering a distance of 10t km.
When Anil turned back after 't' hours, Bala continued walking towards town Y. At this point:
1. Bala still had to cover a distance of (40 - 10t) km to reach town Y.
2. Anil reached Chetan and then traveled with him towards town Y.
Since Anil and Bala reached town Y at the same time, their travel times should be equal. We can set up the following equation to find 't':
50t = 10(40 - 10t)
Simplifying the equation:
50t = 400 - 100t
150t = 400
t = 400 / 150
t = 8/3
Therefore, Anil turned back after approximately 2 hours and 40 minutes (8/3 hours).
To find the time after which Anil turned back, we need to analyze the distances covered by each person during their journey.
Let's assume that Anil turned back after t hours.
During the time Anil and Bala traveled together, their total distance covered is given by:
Distance = Speed * Time
Distance = (50 km/h) * (t hours)
Distance = 50t km
When Anil turned back to pick up Chetan, the distance traveled by Anil would be the same from the previous calculation, but the distance traveled by Chetan would be different. Chetan has been walking the whole time, so his distance traveled is:
Distance = Speed * Time
Distance = (10 km/h) * (t hours)
Distance = 10t km
When Bala continued on foot, he traveled the remaining distance to town Y. Let's denote the remaining distance as d km. Since the total distance from X to Y is 40 km, the distance covered by Bala would be:
Distance = Total Distance - Distance covered by Anil
d = (40 km) - (50t km)
d = 40 km - 50t km
Now, the time taken by Bala to travel the remaining distance can be calculated using his walking speed:
Time = Distance / Speed
Time = (d km) / (10 km/h)
Time = (40 km - 50t km) / 10 km/h
Since Anil and Bala reached town Y at the same time, their total times taken should be equal. Therefore, we can set up the following equation:
Time taken by Anil = Time taken by Bala
t hours = (40 km - 50t km) / 10 km/h
To solve this equation and find the value of t, we can simplify and solve for t:
10t = 40 - 50t
60t = 40
t = 40/60
t = 2/3 hours
Therefore, Anil turned back after 2/3 hours or approximately 40 minutes.