Question

A boat can row 20 km upstream in the same time as the boy covers 10 km distance between home and office and then return home with an average speed of 4 km/hr. if the downstream speed of boat is four times speed of current, find speed of boat in still water (in km/hr) ?

Answer 1

20plus10plus4=20+10+4=34

Answer 2

Answer:

Hence, speed of boat in still water is:

7.5 km/h.

Step-by-step explanation:

If the speed of a boat in still water is u km/hr and the speed of the stream or current is v km/hr, then:

Speed downstream = (u + v) km/hr.

Speed upstream = (u - v) km/hr.

Now, it is given that:

A boat can row 20 km upstream in the same time as the boy covers 10 km distance between home and office and then return home with an average speed of 4 km/hr.

Hence, the time taken by boy is:

$Total \ Time=\dfrac{Total \ time}{Average \ Speed}$

Hence,

$Total \ Time=\dfrac{Total \ time}{Average \ Speed}$

Hence,

$Total \ time=\dfrac{20}{4}=5km/h$

This means:

$u-v=5$

and,

Downstream speed=4v

( since, the downstream speed of boat is four times speed of current )

Hence,

$4v=u+v\\\\4v-v=u\\\\u=3v$

Hence, using equation (1) we have:

$3v-v=5\\\\2v=5\\\\v=\dfrac{5}{2}=2.5\ km/h$

and,

$u=3\times 2.5\\\\u=7.5 \ km/h$

Hence, speed of boat in still water is:

7.5 km/h