- A motor boat whose speed is 18 km/h in still water takes 1 hour more
- A Motorboat Whose Speed in Still Water Is 18 Km/h, Takes 1 Hour More to Go 24 Km Upstream Than to Return Downstream to the Same Spot. Find the Speed of the Stream.[Solved]
- A motor boat whose speed is 18 km/h in still water takes 1 hr.
- A motorboat whose speed in still water is 18 km / h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
- a motorboat whose speed is 18 km/h in still water
- 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.
A motor boat whose speed is 18 km/h in still water takes 1 hour more
Transcript Question 8 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. Given that speed of the boat = 18 km/ hr. Let the speed of the stream = x km / hr. Given that Time taken upstream is 1 hour more than time taken downstream Time upstream = Time downstream + 1 24/((18 − 𝑥)) = 24/((18 + 𝑥)) + 1 24/((18 − 𝑥)) – 24/((18 + 𝑥)) = 1 (24(18 + 𝑥) − 24(18 − 𝑥))/((18 − 𝑥)(18 + 𝑥)) = 1 24((18 + 𝑥) − (18 − 𝑥))/((18 − 𝑥)(18 + 𝑥)) = 1 24(18 + 𝑥 − 18 + 𝑥)/((18 − 𝑥)(18 + 𝑥)) = 1 24(2𝑥)/((18 − 𝑥)(18 + 𝑥)) = 1 48𝑥/((18 − 𝑥)(18 + 𝑥)) = 1 48x = (18 – x) (18 + x) 48x = 182 – x2 48x = 324 – x2 x2 + 48x – 324 = 0 Comparing equation with ax2 + bx + c = 0, Here a = 1, b = 48, c = –324 We know that D = b2 – 4ac D = (48)2 – 4 × 1 × (–324) D = 2304 + 4 × 324 D = 2304 + 1296 D = 3600 So, the roots to equation are x = (−𝑏 ± √𝐷)/2𝑎 Putting values x = (−(48) ± √3600)/(2 × 1) x = (− 48 ± √(60 × 60))/(2 × 1) x = (− 48 ± 60)/2 Solving So, x = 6 & x = – 54 Since, x is the speed , so it cannot be negative So, x = 6 is the solution of the equation Therefore, speed of the stream (x) = 6 km /hr. Show More
A Motorboat Whose Speed in Still Water Is 18 Km/h, Takes 1 Hour More to Go 24 Km Upstream Than to Return Downstream to the Same Spot. Find the Speed of the Stream.[Solved]
A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. The question is a real-life application of Answer: The speed of the stream is 6km/hr. Let's explore the water currents. Explanation: Let the speed of the stream be xkm/hr Given that,the speed boat in still water is 18km/hr. Sspeed of the boat in upstream = (18- x) km/hr Speed of the boat in downstream = (18 + x) km/hr It is mentioned that the boattakes 1 hour more to go 24 km upstream than to return downstream to the same spot Therefore, One-way Distance traveled by boat (d) = 24km Hence, Time in hour T upstream= T downstream+ 1 [distance /upstream speed ] =[distance / downstream speed] + 1 [ 24/ (18 - x) ] = [ 24/ (18 + x) ] + 1 [ 24/ (18 - x) -24/ (18 + x) ] =1 24[1/ (18 - x) -1/(18 + x) ] = 1 24 [ ] = 1 ⇒ 48x =324- x 2 ⇒x 2+ 48x - 324 = 0 ⇒x 2+ 54x - 6x- 324 = 0----------> (by splitting the middle-term) ⇒ x(x + 54) - 6(x + 54) = 0 ⇒ (x + 54)(x - 6) = 0 ⇒ x = -54or 6 As speed to stream can never be negative, we consider the speed of the stream (x) as 6km/hr. Thus, thespeed of the stream is 6km/hr.
A motor boat whose speed is 18 km/h in still water takes 1 hr.
Let the speed of the stream be x km/h. The speed of the boat upstream = (18 – x) km/h and The speed of the boat downstream = (18 + x) km/h. The time taken to go upstream =distance / speed = 24/18-x hours. The time taken to go downstream =distance / speed = 24/18+x hours According to the question, Since x is the speed of the stream, it cannot be negative. Therefore, x = 6 gives the speed of the stream = 6 km/h.
A motorboat whose speed in still water is 18 km / h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Let the speed of the stream be x km/hr Speed of the boat upstream = Speed of boat in still water - Speed of the stream ∴ Speed of the boat upstream = (18-x) km/hr Speed of the boat downstream = Speed of the boat still water + Speed of the stream ∴ Speed of the boat upstream = (18+x) km/hr Time of upstream journey = Time for downstream journey + 1 hr ∴ D i s t a n c e c o v e r e d u p s t r e a m S p e e d o f t h e b o a t u p s t r e a m = D i s t a n c e c o v e r e d d o w n s t r e a m S p e e d o f t h e b o a t d o w n s t r e a m + 1 h r ⇒ 24 k m ( 18 − x ) = 1 ⇒ 24 18 − x − 24 18 + x = 1 ⇒ 432 + 24 x + 432 + 24 x ( 18 − x ) ( 18 + x ) = 1 ⇒ 48 x = 324 − x 2 ⇒ x 2 + 48 x − 324 = 0 ⇒ x ( x + 54 ) − 6 ( x + 54 ) = 0 ⇒ ( x + 54 ) ( x − 6 ) = 0 ⇒ x + 54 = 0 o r x − 6 = 0 ⇒ x = − 54 o r x = 6 ∴ x=6 (Speed of the stream cannot be negative) Thus, the speed of stream is 6 km/hr.
a motorboat whose speed is 18 km/h in still water
People Also Read: How to use A Motorboat Whose Speed in Still Water Is 18 Km/h, Takes 1 – Cuemath A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. The question is a real-life application of linear equations in two variables.
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.
Hint: Use the fact that speed of upstream is the difference of speed of boat in still water and speed of stream and speed of downstream is sum of speed of boat in still water. Then use the formula, $\text-6s+54s-324=0$ Now on factoring we get, $(s-6)(s+54)=0$ So, s is equal to 6 and – 54 as s represents speed so it can’t be negative. Hence, s is 6. Hence, Speed of the stream is 6 km/hr. Note: Students should know the relation between speed of upstream and downstream in terms of speed of boat in still water and speed of stream.
