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
⇒ Time taken to travel the second half = (10 - x) hr
∵ Distance = Time * Speed
Distance covered in the first half = 21x
Distance covered in the the second half = 24(10 - x)
∵ Distance covered in the the first half = Distance covered in the the second half
⇒ 21x = 24(10 - x)
⇒ 45x = 240
⇒ x = 16/3
Total Distance = 2 * 21(16/3) = 224 Km [∵ multiplied by 2 as 21x was the 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:
On solving we will get:
t = 10/3 hrs and v = 12 km/hr
So, distance = (10/3) * 12 = 40 km
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.
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?
Let Anil takes x hrs.
⇒ Arun takes x+2
If Arun doubles the speed, he will take x-1 hrs
⇒ He needs 3 hours less.
∵ Double speed means half time.
∴ Half of the time required by Arun to cover 30 km = 3 hours
⇒ Time required by Arun to cover 30 km = 6 hour
Thus, Arun's speed = 30/6 = 5 km/h
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 = 2 + 3 = 5 rounds per hour
(∴ they walk in opposite directions)
⇒ 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
∴ They cross each other 7 times before 9.30 a.m
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) = 9/2 hrs
∴ Average speed = 320 x (2/9) = 71.11 km/hr.
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 + 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 * 7 * (75 / 5) * 126
⇒ x = 35 km/hr
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 question, we need to get the relative speed between them.
The relative speed of the boys = 5.5 – 5 = 0.5 km/h
The distance between them is 8.5 km.
Time = Distance/Speed
Time = 8.5/0.5 = 17 hrs
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
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) = 2 m/s
i.e. Speed = 2 x (18/5) km/hr = 7.2 km/hr