Advertisements
Advertisements
Question
Choose the most appropriate option
A man rows to a place 45 k.ms distant and back in 12 hours. He realises that he can row 5 k.ms downstream at the same time as 3 k.ms against the stream. The velocity of the stream is:
Options
4 k.ms/hr
1.5 k.ms/hr
1 k.m/hr
2 k.ms/hr
Advertisements
Solution
2 k.ms/hr
Explanation:
Suppose that he moves 5 km downstream in x hours
Then, Speed downstream`="distance"/"Time"`
`=5/"x"` km/hr
Here, he can row 5 km with the stream at the same time as 3 km against the stream
i.e. Speed upstream`=3/5` of speed downstream
Speed upstream`=3/"x"` km/hr
He rows to a place 45 km distant and comes back in 12 hours.
`⇒41/((5/"x"))45/((3/"x"))=12`
⇒ 9x + 15x = 12
⇒ 3x + 5x = 4
⇒ 8x = 6
∴`"x"=4//8=1//2`
Hence. Speed downstream `5/"x"=5/((1/2))` = 10 km / hr
Speed upstream`=3/"x"=3/((1/2))` = 6 km/hr
∴ Ratio of stream`=1/2(10-6)`
`=1/2xx4`= 2 km/hr
APPEARS IN
RELATED QUESTIONS
A car driver increases the average speed of his car by 3 km/hr every hour. The total distance travelled in 7 hours if the distance covered in the first hour was 30 km, is
A man covers a certain distance between his house and office on a Scooter. Having an average speed of 30 km/hr, he reaches the office late by 10 minutes. However, with a speed of 40 km/hr, he reaches his office 5 minutes earlier. The distance between his house and office is
A streamer goes downstream from one port to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of the stream is 2 km/h, the distance between the two ports is
A man covered a certain distance at some speed. Had he moved 3 km/h faster, he would have taken 40 min less. If he had moved 2 km/h slower, he would have taken 40 min more. The distance (in km) is
Robert is travelling on his cycle and has calculated to reach point A at 2 pm if he travels at 10 km/h, he will reach there at 12 noon if he travels at 15 km/h. At what speed must he travel to reach A at 1 pm?
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 s. If one is moving twice as fast the other, then the speed of the faster train is
Mr. X drives to his office at an average speed of 48 km per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office?
A car completes a certain journey in 8 h. It covers half the distance at 40 km/h and the rest at 60 km/h. The length of the journey is
A truck covers 448 km in 8 hours. The average speed of a bicycle is `1/4` th of the average speed of the truck. How much distance will the bicycle cover in 7 hours?
A 300 metre long train moving with an average speed of 126 km/hr. crosses a platform in 24 seconds. A man crosses the same platform in 5 minutes. What is the speed of man in metre/second?
