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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

by Level 11 User (80.9k points)

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