A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Let time taken to travel the first half = x hr
Then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21*x [because, distance = time*speed]
Distance covered in the the second half = 24(10 - x)
Distance covered in the the first half = Distance covered in the the second half
So, 21x = 24(10 - x)
=> 45x = 240
=> x = 16/3
Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21*x was distance of half way]
A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?
According to given condition
vt = (v + 3)(t - 2 / 3)
vt = (v - 2)(t + 2 / 3)
here v is velocity in kmph, t is time in hours and 2 / 3 is value of 40 min in hour.
On solving we will get
t = 10 / 3 and
v = 12
So, distance = (10 / 3) * 12
= 40 kms
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Due to stoppages, it covers 9 km less in an hour.
Time taken to cover 9 km =(9/54 )*60 min = 10 min.
A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
Relative speed = Speed of A + Speed of B (∴ they walk in opposite directions) =2+3 = 5 rounds per hour
Therefore, they cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 8 a.m. to 9.30 a.m. = 1.5 hour
Hence they cross each other 7 times before 9.30 a.m
In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?
If Arun doubles his speed, he needs 3 hour less.
Double speed means half time.
Hence, half of the time required by Arun to cover 30 km = 3 hour
i.e., Time required by Arun to cover 30 km = 6 hour
Arun's speed = 30 / 6 = 5 kmph
A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. What is the actual speed of the car?
Time taken = 1 hr 40 min 48 sec
= 1 hr 40 x 4 / 5 min
= 1 + 51 / 75 hrs
= 126 / 75 hrs.
Let the actual speed be x km/hr.
Then, 5 / 7* x *126 / 75 = 42
⇒ x = 42 x 7 x (75 / 5) x 126
⇒ x = 35 km/hr
A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
Total time taken = (160 / 64 + 160 / 80)hrs. = 9 / 2 hrs.
∴ Average speed = (320 x 2 / 9) km/hr = 71.11 km/hr.
Q. A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways, is:
Given that time taken for riding both ways will be 2 hours lesser than the time needed for walking one way and riding back.
From this, we can understand that
Time needed for riding one way = time needed for walking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence, the time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Speed = Distance/ Time
Speed = (600 / 5 x 60) m / sec
= 2 m/sec
= 2 x (18/5) km/hr
= 7.2 km/hr