Boats and Streams Examples 1

In this class, We discuss Boats and Streams Examples 1.

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Example 1:

There is a road beside a river.

Two friends started from place A, moved to a temple situated at place B and then returned to place A.

One moves on a cycle at 12 kmph, and the other sails on a boat at ten kmph. The river flows at a speed of 4 kmph.

Which of the two friends will return to place A first?

Solution:

The below diagram shows the graphical intuition of the example.

Two friends moved from place A to B and returned to A.

Who will come first?

Who has the maximum speed will come first.

If they moved to B with one speed and returned to A with another speed, then We go with average speed. We discussed the basics of average speed formulas.

The cyclist moves at a speed of 12 kmph.

Both sides move at the same speed. So average speed = 12 kmph.

Boat move downstream = 10 + 4 kmph. = 14 kmph.

Upstream = (10-4) kmph. Six kmph.

Average speed = 2xy/(x+y) Formula explained in speed and distance.

Average speed = 2*14*6/(14+6) = 8.4 kmph.

The cycle comes first.

Example 2:

A man can row 7 1/2 kmph in still water.

If in a river running at 1.5 kmph, it takes him 50 minutes to row to a place and back.

How far is the place?

Solution:

The below diagram shows the graphical intuition for the example.

Given Time and Speed.

Assume, Distance = x.

downstream = 7.5 + 1.5 = 9 kmph

Upstream = 7.5 – 1.5 = 7 kmph.

Time = Distance/ Speed

The time to travel both sides is 50 minutes.

Convert to hours = 50/60

x/9 + x/7 = 50/60

x = 3 kilometres.