A motorboat, whose speed is 15 km/h in still water, goes 50 km downstream and comes back in a total of 7 hours 30 minutes. What is the speed of the stream (in km/h)?

Question

Accepted Answer

Let the speed of the stream be x km/h.

Speed downstream = (15 + x) km/h
Speed upstream = (15 - x) km/h

Distance downstream = 50 km
Distance upstream = 50 km

Total time = 7 hours 30 minutes = 7.5 hours

Time downstream + Time upstream = Total time
=> 50 / (15 + x) + 50 / (15 - x) = 7.5

Multiply both sides by (15 + x)(15 - x):
50(15 - x) + 50(15 + x) = 7.5(15 + x)(15 - x)

Expand:
50*15 - 50x + 50*15 + 50x = 7.5(225 - x^2)

Simplify left side:
750 - 50x + 750 + 50x = 7.5(225 - x^2)

The -50x and +50x cancel out:
1500 = 7.5(225 - x^2)

Divide both sides by 7.5:
1500 / 7.5 = 225 - x^2

Calculate:
200 = 225 - x^2

Rearranged:
x^2 = 225 - 200 = 25

Therefore, x = 5 or x = -5 (speed cannot be negative)

So, the speed of the stream is 5 km/h.

However, the given answer is 9 km/h, so let's re-check calculations:

Recalculate the step where we multiplied:
50(15 - x) + 50(15 + x) = 7.5(15 + x)(15 - x)

Left side:
50*15 - 50x + 50*15 + 50x = 750 - 50x + 750 + 50x = 1500

Right side:
7.5(225 - x^2) = 1687.5 - 7.5x^2

So equation is:
1500 = 1687.5 - 7.5x^2

Bring all terms to one side:
7.5x^2 = 1687.5 - 1500 = 187.5

Divide both sides by 7.5:
x^2 = 187.5 / 7.5 = 25

x = 5 km/h

So the speed of the stream is 5 km/h.

Hence, the correct answer is option 2: 5 km/h.

Answer

Answer

Answer