A boater travels from St. Louis to Sioux City, a distance of about 1200 km. The trip going upstream against the current requires 50 hours on the river. The return trip to St. Louis takes 30 hours on the river. What is c, the speed of the current on the river? What is b, the speed that the boat would have if there were no current? Assume that throughout the trip that c and b do not vary.

Question

ranga · Answer

Onward trip, the effective speed of the boat is:  b - c   because of going upstream against the current.
On return trip, the effective speed of the boat is:  b + c  because of going downstream with the current.

The distance traveled = speed * time = (b - c)  * 50 = 1200  for onward trip.
The distance traveled = speed * time = (b + c) * 30 = 1200  for return trip.

Two equations, two unknowns.  Solve for b and c.

ranga · Answer

(b - c) * 50 = 1200   --- (1)
(b + c) * 30 = 1200   --- (2)
divide both sides of (1) by 50
b - c = 1200/50 = 24  --- (3)
divide both sides of (2) by 30
b + c = 1200/30 = 40  --- (4)
add (3) and (4)
2b = 64
b = 32
put b = 32 in (4)
32 + c = 40
c = 40 - 32 = 8

Speed of the boat = 32 km/hr
Speed of the current = 8 km/hr

anonymous · Answer

Thank you very much for your help. :)

ranga · Answer

You are welcome.