*A motorboat takes 5 hours to travel 100 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?*

Let S be the distance travelled by the boat, both upstream and downstream = 100 miles

Let Vc be the speed of the current

Let Vm be the speed of the motorboat (in still water)

Let Vu be the speed of the boat as it travels upstream = Vm - Vc

Let Tu be the time to travel upstream = 5 hrs

Let Vd be the speed of the boat as it travels downstream = Vm + Vc

Let Td be the time to travel downstream = 2 hrs

Travelling upstream

S = Vu*Tu = 5Vu = 5(Vm - Vc)

Travelling downstream

S = Vd*Td = 2Vd = 2(Vm + Vc)

Substituting Values,

100 = 5Vm - 5Vc

100 = 2Vm + 2Vc

Substituting for Vm = 50 - Vc into the 1st eqn above,

100 = 5(50 - Vc) - 5Vc

100 = 250 - 5Vc - 5Vc

10Vc = 150

**Vc = 15 mph**

**Vm = 35 mph**