Question

Example 15: A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream​

Answer 1

Answer:

Let the speed of stream be x km/hr

So,

Speed of upstream =(18-x) km/hr

Spped of boat downstream = (18+x) km/hr

Time taken to go upstream

$= \frac{24}{18 + x}$

Similarly, time taken to go downstream =

$\frac{24}{18 - x}$

ATQ,

$\frac{24}{18 - x} - \frac{24}{18 + x} = 1 \\ \\ \to \: 24(18 + x) - 24(18 - x) \\ = (18 - x) (18 + x) \\ \\ = {x}^{2} + 48x - 324 = 0 \\ \\ \sf \:x = 6 \: or \: {- 54}$

Since x is the speed of the stream, it cannot be negative. So, we ignore the root x=-54.

Therefore, x=6 the speed of stream as 6 km/hr

Hope it helps you from my side

:)

Answer 2

$\huge\red{A}\pink{N}\orange{S} \green{W}\blue{E}\gray{R} =$

Given parameters:

The speed of the motorboat in still water =18 kmph

Let us consider

The speed of the stream = s

Speed of boat upstream = Speed of a boat in still water – the speed of a stream

Speed of boat upstream = 18 – s

Speed of boat downstream = Speed of a boat in still water + speed of a stream

Speed of boat downstream = 18 + s

Time is taken for upstream = Time taken to cover downstream + 1

time =distance/speed

24/ (18 – s) = [24/(18 + s)] + 1

24(18+s) = 24(18−s) + (18−s)(18+s)

s2 + 48s − 324 = 0

s2 + 54s − 6s − 324 = 0

(s+54)(s−6) = 0

s = 6,−54 but s ≠−54

Since the speed of steam cannot be negative.

∴ s = 6km/hr