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

The distance between the two towns is 60 miles.

Explanation:

Let the distance between A and B is d.

A to B , t = 2 hour

B to A , t' = 1.5 hour

Speed of current, u = 5 mph

Let the speed of ferry is v.

distance = speed x time

d = (v - 5) x 2 = (v + 5) x 1.5

2 v - 10 = 1.5 v + 7.5

0.5 v = 17.5

v = 35 mph

So, the distance is

d = (35 - 5) x 2 = 60 miles.

Answer 2

Answer: 60 miles

Explanation:

Given

It takes ferry 2 hours to travel to town A and only
`1.5\ hr` to travel back to town B.

Speed of current is
`u=5\ mph`

Suppose the speed of the ferry is
`v` mph

Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.

`\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph`

Distance between the towns is
`2* (35-5)=60\ \text{miles}`