Question

Please help me . I don’t understand this question.A boat whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Answer 1

Answer:

5 km/hr

Step-by-step explanation:

Question is:

• A boat whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Let's clarify:

• A boat whose speed in 15 km/hr in still water- imagine it is boat moving in the lake, water is not affecting it's movement

• Different condition when boat is moving in the river. A river has a water movement which is called stream or current. It has own speed.

• Boat is moving downstream- in this case the speed of the stream helps the boat to increase its speed and speeds are added up.

• Boat is moving upstream- in this case the boat is moving against the stream and as a result its speed is decreased by the speed of the stream

Let's solve the question based on the information we have:

• Boat speed in still water (like in the lake)= 15 km/hr
• The distance= 30 km
• Boat travels downstream and back, so travels 30*2= 60 km
• Time for full travel= 4.5 hrs

Based on the given let's build an equation:

We have boat speed, distance and time known. The unknown is the speed of the stream. Let's call it x

• When boat moves downstream, its speed = 15+x
• When boat moves upstream, its speed= 15-x

With different speed upstream and downstream it takes different time to arrive but we have total time and build our equation on the time calculation.

So, we have:

• 30/15+x- time in travel downstream (note speeds added up)
• 30/15-x - time in travel upstream (note speeds subtraction)

In total, time is equal to sum of time spent on downstream and upstream:

• 30/15+x + 30/15-x=4.5

• 4.5(15²-x²)=30(15-x+15+x)
• 4.5(225-x²)=900
• 4.5x²=1012.5-900
• x²=25
• x=5 km/hr

Solved!

Speed of the stream is 5 km/hr

Hope you can now answer similar questions. Let me know if anything is not clear.