Question

A boat has a speed of 9 mph in calm water. It takes the boat 4 hours to travel upstream but only 2 hours to travel the same distance downstream. Which equation can be used to find c, the speed of the current? 2(9 – c) = 4(9 + c) 9 + c = 4(9 – c) 9 – c = 2(9 + c) 4(9 – c) = 2(9 + c)

Answer 1

speed of boat = 9 mph

speed of current = c mph  

against current speed = 9-c---------------time = 4 hours

with current speed = 9+c------------------time = 2 hours  

d=rt  

4(9-c) = 2(9+c)  

Answer 2

Solution:

The equation to find the value of c is 4(9-c)=2(9+c)

Explanation:

Let us suppose the speed of the current is c.

Then, we have

The upstream speed of the boat is 9-c

The downstream speed of the boat is 9+c

Now, we know the relation between speed, distance and time which is given by

$\text{Distance}=\text{Speed}\times \text{time}$

Using this relation, we have

Upstream distance = 4(9-c)

Downstream distance = 2(9+c)

These two distance should be equal. Hence, we have

4(9-c)=2(9+c)

Thus, the required equation is given by

4(9-c)=2(9+c)