A motorboat travels 62 km in 2 hours going upstream It trave

A motorboat travels 62 km in 2 hours going upstream. It travels 86 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current? Rate of the boat in still water: km/h Rate of the current: km/h

Solution

A motorboat travels 62 km in 2 hours going upstream and 86 km in 2 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?
:
Let x = speed of boat in still water
Let y = speed of the current
then
(x-y) = Upstream speed
(x+y) = downstream speed
:
Write a distance equation for each trip; (Distance = time * speed)
:
Upstream trip equation:
2(x - y) = 62
Simplify, divide both sides by 8; resulting in:
x - y = 31
:
Downstream trip equation:
2(x + y) = 86

Simplify, divide both sides by 2: resulting in:
x + y = 43
:
Use these two equations for elimination:
x - y = 31
x + y = 43
--------------adding eliminates y, find x.

2x = (31+43)

2x = (74)

x=37 km/hr in still water

find y using x+y =43

37+y=43

y=43-37

y=6 km/hr is the current

checking solution:

2(37-6) =62

2(31)=62

62=62 (so true)