Advertisement Remove all ads

A Motor Boat Whose Speed in Still Water is 18 Km/Hr Takes 1 Hour More to Go 24 Km up Stream that to Return Down Stream to the Same Spot. Find the Speed of the Stream. - Mathematics

Answer in Brief

A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.

Advertisement Remove all ads

Solution

Let the speed of the stream be x km/hr.
speed of the boat in still water = 18 km/hr.
Total Distance = 24 km.
We know that,
Speed of the boat up stream = speed of the boat in still water − speed of the stream
                                            = (18 − x) km/hr
Speed of the boat down stream = speed of the boat in still water + speed of the stream
                                                  = (18 + x) km/hr
Time of up stream journey = t1 = \[\frac{24}{18 - x}\]

Time of down stream journey = t2 = \[\frac{24}{18 + x}\]

According to the question,
 t1 − t2 = 1 hr

\[\Rightarrow \frac{24}{18 - x} - \frac{24}{18 + x} = 1\]

\[ \Rightarrow \frac{24(18 + x - 18 + x)}{(18 - x)(18 + x)} = 1\]

\[ \Rightarrow \frac{24(2x)}{(18 )^2 - x^2} = 1\]

\[ \Rightarrow 48x = 324 - x^2 \]

\[ \Rightarrow x^2 + 48x - 324 = 0\]

\[ \Rightarrow x^2 + 54x - 6x - 324 = 0\]

\[ \Rightarrow x(x + 54) - 6(x + 54) = 0\]

\[ \Rightarrow (x - 6)(x + 54) = 0\]

\[ \Rightarrow x - 6 = 0 \text { or } x + 54 = 0\]

\[ \Rightarrow x = 6 \text { or } x = - 54\]

Since, speed cannot be negative.
Thus, speed of the stream is 6 km/hr.

Concept: Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.8 | Q 14 | Page 59
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×