Town P and Q are 265 km apart. Car A started from P at 60 km/hr at 8.00 am towards Q. Car B started from Q at 40 km/hr at 10.00 am. B stopped for half an hour. A stopped for 28 minutes at town S which is at a distance of 210 km from P. Find the time at which B crossed A.
A, Starts from P, S=60kmph, At 11.30 AM (Rest of 28mins.)
B, Starts from Q, S=40kmph, At 11.00 AM (Rest of 30mins.)
At 8AM, distance between is 265km
At 10AM, distance between is 145km as A travels 120km in 2hrs
At 11AM, distance between is 45km as A&B travel 100km
At 11.30AM, distance b/w is 15km at A travels 30km
Now d=15,s=40(bec. A is resting)
t=22.5 minutes
Thus, 11.30+22.5 min=11.52.30AM
To find the time at which Car B crossed Car A, we need to calculate the time taken by each car to reach the meeting point.
Let's start by finding the time taken by Car A to reach town S:
Distance between P and S = 210 km
Speed of Car A = 60 km/hr
Time taken by Car A to reach town S = Distance / Speed = 210 km / 60 km/hr
= 3.5 hours
Next, we need to find the time taken by Car B to reach town S:
Distance between S and Q = Distance between P and Q - Distance between P and S
= 265 km - 210 km
= 55 km
Speed of Car B = 40 km/hr
Time taken by Car B to reach town S = Distance / Speed = 55 km / 40 km/hr
= 1.375 hours (or 1 hour and 22.5 minutes)
Now, let's calculate the time at which Car A reached town S:
Car A started from P at 8:00 am and takes 3.5 hours to reach town S.
Therefore, Car A reached town S at 8:00 am + 3.5 hours = 11:30 am.
Now, let's calculate the time at which Car B reached town S:
Car B started from Q at 10:00 am and takes 1 hour and 22.5 minutes to reach town S.
Therefore, Car B reached town S at 10:00 am + 1 hour 22.5 minutes = 11:22.5 am.
Since Car B reached town S earlier than Car A, Car B crossed Car A at town S.
Hence, Car B crossed Car A at 11:22.5 am.
To find the time at which Car B crosses Car A, we need to calculate the time taken by each car to reach the meeting point.
Let's calculate the time taken by Car A to reach the meeting point at town S.
Distance between P and S = 210 km
Speed of Car A = 60 km/hr
Time taken by Car A to reach S = Distance/Speed = 210/60 = 3.5 hours
Now, let's calculate the meeting time when Car A reaches town S.
Car A started from P at 8.00 am.
Car A takes 3.5 hours to reach S.
So, the meeting time for Car A at town S = Starting time + Travel time = 8.00 am + 3.5 hours = 11.30 am
Now, let's calculate the time taken by Car B to reach the meeting point.
Distance between S and Q = Total distance between P and Q - Distance between P and S.
Distance between S and Q = 265 km - 210 km = 55 km
Speed of Car B = 40 km/hr
Time taken by Car B to reach Q = Distance/Speed = 55/40 = 1.375 hours or 1 hour and 22.5 minutes
Now, let's calculate the crossing time.
Car B started from Q at 10.00 am.
Car B takes 1.375 hours to reach the meeting point after stopping for half an hour.
So, the crossing time of Car B = Starting time + Travel time + Stopping time = 10.00 am + 1 hour and 22.5 minutes + 0.5 hours = 11.52 am
Therefore, Car B crosses Car A at 11.52 am.
A went 210 km in 3.5 hr (11:30)
A stopped till 11:58
A then went on.
So, A's position x in terms of time elapsed from 8:00 is
x =
60t for 0 <= t <= 7/2
210 for 3.5 <= t <= 3 29/30
210+60(t-3 29/30) for t > 3 29/30
A reached Q at 11:58+0:55 = 12:53
B's distance y is thus
y = 40(t-2)
y=210 at t=7.25, or 15:15
B never passed A, since it started later and was going slower.
I suspect a typo. Maybe the cars are backwards?