time speed and distance

Question

Shyam can row 36 km upstream inn 4 hours. If the speed of the stream is 3 kmph then find how far he can go downstream in 6 hours

Answer 1

Remember that distance = (rate)(time). We'll write two equations: one for Shyam rowing upstream (against the current) and one for Shyam rowing downstream (with the current).

 

 

 

UPSTREAM:

 

Shyam travels a distance of 36 km. We're not told the rate at which he rows, so call that r. That means he travels upstream (against the current) at a rate of r - 3 kph. Shyam travels a time of 4 hours. So:

 

36 = (r - 3)(4)

 

 

 

DOWNSTREAM:

 

Shyam travels an unknown distance d. He travels downstream (with the current) at a rate of r + 3 kph. Shyam travels a time of 6 hours. So:

 

d = (r + 3)(6)

 

 

 

Now you have a system of equations:

 

36 = (r - 3)(4)

d = (r + 3)(6)

 

 

 

Simplify the first equation to solve for r:

 

36 = 4r - 12

48 = 4r

12 = r

 

Plug that into the second equation to solve for d:

 

d = (12 + 3)(6)

d = (15)(6)

d = 90

 

 

 

Shyam can travel a distance of d = 90 km downstream in 6 hours.