Question

A boat travels 500 km in eight hours going upstream and 430 km in five hours going downstream. Find the speed of the boat in still water, and find the speed of the current.

Answer 1

Let x = speed of boat in still water
Let y = speed of the current
then
(x-y) = Upstream speed
(x+y) = downstream speed

Then the distance equation for each trip is (Distance = time x speed)

Upstream trip equation:
8(x - y) = 500
Dividing both sides by 8 we get,
x - y = 62.5
Downstream trip equation:
5(x + y) = 430
Dividing both sides by 5 we get
x + y = 86

Solve two equations
x - y = 62.5
x + y = 86
--------------
2x = 148.5
x = 74.25
x = 74.25 km/hr in still water

To find y, substitute 71 for x:
74.25 + y = 86
y = 86 - 74.25
y = 11.75 km/hr is the current;