Time and Distance questions
1.A man can row 30 km downstream and returns in the total of 8 hours. If the speed of boat in still water is 4 times speed of current. find the speed of current.
2.A man started 15 minutes late and travelling at a speed which is 5/4th of his usual speed he reached office 20 min early. Find his usual time of journey.
3. A distance between two stations P and Q is 120 km.A train starts from P to Q at 9:00 am with the speed of 40km/hr while other starts from Q to P at 10:00 am with speed of 40km/hr. After one hour first train halts at station for 15 min before starting its journey again but 2nd train does not halt anywhere.At what time trains meet?
2.A man started 15 minutes late and travelling at a speed which is 5/4th of his usual speed he reached office 20 min early. Find his usual time of journey.
Sol: Let the initial speed and time be V km/min and T min
And the final speed and time is 5v/4 km/min and time is (T-35) min.
The distance is same .
So, V xT=5V x (T-35)/4
Solving, T=175 minutes= 2 hours and 55 minutes.
Ans: 2hr 55 mins.
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3. A distance between two stations P and Q is 120 km.A train starts from P to Q at 9:00 am with the speed of 40km/hr while other starts from Q to P at 10:00 am with speed of 40km/hr. After one hour first train halts at station for 15 min before starting its journey again but 2nd train does not halt anywhere.At what time trains meet?
Sol.At 10:15 am, first train 40km far away from point P and second train 10km far away from point Q.
then at 10:15 am, distance b/w these two trains is (120-50) = 70km
time= 70/(40+40) = 7/8 hr or 52 min and 30sec.
trains meet to each other at 11:07:30 am (10:15 am + 52 min and 30sec)
3) A distance between two stations P and Q is 120 km.A train starts from P to Q at 9:00 am with the speed of 40km/hr while other starts from Q to P at 10:00 am with speed of 40km/hr. After one hour first train halts at station for 15 min before starting its journey again but 2nd train does not halt anywhere.At what time trains meet?
Sol: As the speed of both the trains is 40km/hr. The first train will cover 40 km in 1 hour and take a rest of 15 mins. So the first train will cover 40 km till 10:15.
And the second train will start at 10:00 and will cover a distance of 10 km till 10:15.
The distance left between the two trains=(120-40-10)=70 km.
As both the trains are travelling with the same speed,the distance covered by both the train to meet=70/2=35 km.
So, the time taken to cover 35 km=35/40 hr
=35x 3600/40=3150 sec.
=3150/60=52.5 mins.=10.15 am + 52.5 mins.
= 11:07:30 am
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Sugandha Chatterjee
just lemme kno y is it T-35. he started 15 min late.. so (T-15). and arrived 20 min earlier..(T-15+20)= (T+5)..
kindly give the logic behind this..
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Sugandha Chatterjee
just lemme kno y is it T-35. he started 15 min late.. so (T-15). and arrived 20 min earlier..(T-15+20)= (T+5)..
kindly give the logic behind this..
Suppose the usual time taken by him to reach is T hours.
Now he start 15 min late so time taken to reach will be 15 min less tha usual .Also he reaches 20 minutes early..so the trime taken reduces further by 20 minutes .
So all an all 35 less time taken as usual.
I think now you might have got this..
Any other query is most welcomed..
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1.A man can row 30 km downstream and returns in the total of 8 hours. If the speed of boat in still water is 4 times speed of current. find the speed of current.
Sol: Let the speed of boat be u km/hr and the straem be v km/hr.
A/q, 30/(u+v)+30/(u-v)=8...(i)
Also, u=4v...(ii)
From (i) and (ii)-
u=8km/h and v=2km/hr.
Ans: 2km/hr
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