Advertisements
Advertisements
Question
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream is 5 hours. Fid the speed of the stream
Solution
Speed of the boat in still water =8 km/ hr.
Let the speed of the stream be x km/hr.
∴Speed upstream=`(8-x)`km/hr.
Speed downstream =`(8+x)` km/hr.
Time taken to go 22 km downstream=`22/(8+x) hr`
Time taken to go 15 km upstream=`15/((8-x))hr`
According to the question:
⇒`22/(8+x)+15/(8-x)=5`
⇒`22/(8+x)+15/(8-x)-5=0`
⇒`(22(8-x)+15(8+x)-5(8-x)(8+x))/((8-x)(8+x))=0`
⇒`176-22x+120+15x-320+5x^2=0`
⇒`5x^2-7x-24=0`
⇒`5x^2-(15-8)x-24=0`
⇒`5x^2-15x+8x-24=0`
⇒`5x(x-3)-8(x-3)=0`
⇒`(x-3) (5x-8)=0`
⇒`x-3=0 or 5x-8=0`
⇒`x=3 or x=8/5`
⇒`x=3` ( ∴Speed cannot be a fraction)
∴Speed of the stream =3 km/ hr
APPEARS IN
RELATED QUESTIONS
The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by `1/15`
. Find the fraction
300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.
Some students planned a picnic. The total budget for food was ₹ 2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by ₹ 20. How many students attended the picnic and how much did each student pay for the food?
A dealer sells an article for ₹ 75 and gains as much percent as the cost price of the article. Find the cost price of the article.
One year ago, man was 8 times as old as his son. Now, his age is equal to the square of his son’s age. Find their present ages.
A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.
A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Two pipes running together can fill a tank in `11 1/9` minutes. If on pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank
separately.
Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km.
What is the speed of Raj’s car?
The speed of a motorboat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more upstream than downstream.
What is the relation between speed, distance and time?
