| 1. |
A boat can travel 16 km downstream in 40 min. If the speed of the stream is three fifth the speed of boat in still water, then what distance the boat can travel upstream in 45 min?1. 4 km2. 3 km3. 4.5 km4. 3.5 km5. 5 km |
|
Answer» Correct Answer - Option 3 : 4.5 km Given: Distance travelled by boat in downstream = 16 km Time boat takes to complete the distance in downstream = 40 min Speed of stream = (3/5) × the speed of boat in still water Formula used: Downstream speed = Speed of boat + Speed of stream Upstream speed = Speed of boat – Speed of stream Speed = Distance/Time Calculation: Let speed of boat in still water be u Let speed of stream be v v = (3/5)u Let downstream speed be a Let upstream speed be b a = 16/40 km/min ⇒ a = (16 × 60)/40 km/h ⇒ a = 24 km/h Downstream speed = Speed of boat + Speed of stream ⇒ a = u + v ⇒ 24 = u + (3/5)u ⇒ 24 = (5u + 3u)/5 ⇒ 120 = (5u + 3u) ⇒ 8u = 120 ⇒ u = 15 km/h v = (3/5)u ⇒ v = 9 km/h Upstream speed = Speed of boat – Speed of stream ⇒ b = u – v ⇒ b = 15 – 9 = 6 km/h Upstream distance covered in 45 min Distance = 6 × (45/60) = 4.5 km ∴ The upstream distance covered by boat in 45 min is 4.5 km. |
|