Question

It took boat to travel from pier A to pier B 5 hours going upstream. It made the return trip downstream in 3 hours and 30 minutes. What is the distance between two piers, if the speed of the current is 3 mph?

Answer 1

the distance between two piers is 70 m

What is upstream and downstream?

• Upstream: When the boat is going against the direction flow of water, then it is called going upstream. When the boat goes upstream then the speed of the boat and the flow of water gets subtracted.
• Downstream:  When the boat is going in the same direction as the direction flow of water, then it is called going downstream. When the boat goes downstream then the speed of the boat and the flow of water gets added.

How to calculate the distance?

Let the distance between the piers be D metre and the speed of the boat be S mph

• the speed of the current is 3 mph

We know that time can be given by the formula ,

$time=\frac{distance}{speed}$

• boat took 5 hours going upstream to travel from pier A to pier B.

∴ we can write

$5=\frac{D}{S-3}$....................(1)

Since the boat is going upstream, the speed got subtracted.

• boat took 3 hours and 30 minutes going downstream to travel from pier A to pier B

∴ we can write

$3.5=\frac{D}{S+3}$.................(2)

Now solving the equations,

From (1),

$S-3=\frac{D}{5}$

⇒$S=\frac{D}{5} + 3$

Putting the value of S in equation (2)

$\frac{7}{2} = \frac{D}{\frac{D}{5}+6 }$

⇒$\frac{7}{2} = \frac{5D}{{D}+30 }$

⇒$10D=7D+210$

⇒D = 70

∴ the distance between two piers is 70 m

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