Question

A certain ferry moves up and down a river between Town A and B. It takes the ferry two hours to travel to Town A and only an hour and thirty minutes to return to Town B. If the current is 5mph how far apart are the two cities?

Answer 1

I believe that the answer is 60 miles

Explanation:

Answer 2

The distance between two cities is 60 miles.

Explanation:

Time taken to travel from B to A = 2 hours

Time taken to travel from A to B = 1.5 hours

Current speed = 5 mph

Let the speed of ferry in still water = u mph

When the ferry moves with the current, it will taken lesser time (i.e. A to B) and when it moves against the current it will take more time (i.e. B to A).

Let the distance between the two cities A and B = D miles

While moving with the current, speed =
`(u+5)\ mph`

While moving against the current, speed =
`(u-5)\ mph`

Formula for Distance = Speed
`*` Time

Distance traveled in each case is same i.e. D.

So,

`D = (u+5) * 1.5 = (u-5) * 2\\\Rightarrow 1.5u+7.5=2u-10\\\Rightarrow 0.5u =17.5\\\Rightarrow u = (175)/(5)\\\Rightarrow u = 35 \ mph`

Now,

`D = (u+5) * 1.5\\\Rightarrow D =(35+5) * 1.5\\\Rightarrow D =(40) * 1.5\\\Rightarrow \bold{D =60\ miles}`

So, the distance between two cities is 60 miles.