A motor boat whose speed is 20 km/h in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of stream.
Answers
☀️ As per the given information, we know that a motorboat whose speed is 20 km/h in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot. As we know that, when the motorboat goes downstream the speed of stream is added to speed of motorboat and when it goes upstream the speed of stream gets subtracted from the speed of motorboat.
❍ In order to find the speed of stream we have to assume the speed of stream and form an equation according to the question. Then, by solving that equation we can find the speed of stream.
- A motor boat whose speed is 20 km/h in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot.
- Find the speed of stream ?
~Information we have ::
- Speed on upstream = ( Speed of motorboat - Speed of stream )
- Speed on downstream = ( Speed of motorboat + Speed of stream )
- Time taken = Total distance covered ÷ Speed
⍟ Let the speed of stream be ‘ x km/h ’
Then we can write as,
Speed,
⟶ Speed of motorboat on upstream = ( 20 - x ) km/h
⟶ Speed of motorboat on downstream = ( 20 + x ) km/h
Time taken,
⟶To cover 48 km upstream = ( 48 ÷ 20-x ) hours
⟶To cover 48 km downstream = ( 48 ÷ 20+x ) hours
- Time taken in the upstream journey - Time taken in the downstream journey = 1 hour
⇢ 48/20 - x - 48/20 + x = 1
⇢ 20 + x - 20 + x/20² - x² = 1/48
⇢ 2x/400 - x² = 1/48
⇢ 2x × 48 = 400 - x²
⇢ x² + 96x - 400 = 0
⇢ x² + 100x - 4x - 400 = 0
{ Factorizing }
⇢ x(x + 100) - 4(x + 100) = 0
⇢ (x - 4)(x + 100) = 0
⇢ x = 4
or
⇢ x = -100
[ Speed cannot be negative so we’ll take 4 as value of x ]
____________
Henceforth,
- Speed of the stream is 4 km/h
See the attachment ⤴️
○ Hope it helps you ❤ ○
