A boat takes 90 minutes less to travel 36 mil | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the speed of the stream be $x$ miles/hour.Speed of the boat in still water = $10$ miles/hour.Downstream speed = $(10 + x)$ miles/hour.Upstream

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) Let the speed of the stream be $x$ miles/hour.Speed of the boat in still water = $10$ miles/hour.Downstream speed = $(10 + x)$ miles/hour.Upstream speed = $(10 - x)$ miles/hour.Time taken to travel $36$ miles upstream = $\frac{36}{10 - x}$ hours.Time taken to travel $36$ miles downstream = $\frac{36}{10 + x}$ hours.Given that the difference in time is $90$ minutes,which is $\frac{90}{60} = 1.5$ hours.Therefore,$\frac{36}{10 - x} - \frac{36}{10 + x} = 1.5$.$\frac{36(10 + x) - 36(10 - x)}{(10 - x)(10 + x)} = 1.5$.$\frac{360 + 36x - 360 + 36x}{100 - x^2} = 1.5$.$\frac{72x}{100 - x^2} = 1.5$.$72x = 1.5(100 - x^2)$.$72x = 150 - 1.5x^2$.$1.5x^2 + 72x - 150 = 0$.Dividing by $1.5$,we get $x^2 + 48x - 100 = 0$.$(x + 50)(x - 2) = 0$.Since speed cannot be negative,$x = 2$ miles/hour.

$A$ boat takes $90$ minutes less to travel $36$ miles downstream than to travel the same distance upstream. If the speed of the boat in still water is $10$ miles/hour,the speed of the stream is.......miles/hour.

Similar Questions

$A$ man can swim in still water at $9.6 \text{ km/hr}$,but takes twice as long to swim upstream as he does downstream. The speed of the stream is ......... $\text{km/hr}$.

$A$ man swimming in a stream which flows at $1 \frac{1}{2} \text{ km/h}$ finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim? (in $\text{km/h}$)

$A$ man moves downstream at a rate of $14\, km/h$ and upstream at a rate of $6\, km/h$. The speed of the boat in still water is........$km/h$.

$A$ man can row at $5 \text{ km/hr}$ in still water. If the velocity of the current is $1 \text{ km/hr}$ and it takes him $1 \text{ hour}$ to row to a place and come back,how far is the place? (in $\text{km}$)

$A$ boat covers a certain distance downstream in $1 \text{ hour}$,while it comes back in $1.5 \text{ hours}$. If the speed of the stream is $3 \text{ km/hr}$,what is the speed of the boat in still water? (in $\text{km/hr}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module