Question: A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
Video Explanation
Explanatory Answer
Speed of motorboat in still water = 24 km/hr
Let speed of stream be x km/hr
Upstream speed of boat = (24 – x)km/hr
Time taken to travel 32 km upstream = \\frac{32}{24 - x})hr
Downstream speed of boat = (24 + x) km/hr
Time taken to travel 32 km downstream = \\frac{32}{24 + x})
The boat takes an hour longer to travel upstream than to travel downstream
i.e., \\frac{32}{24 - x}) = \\frac{32}{24+x}) + 1
\\frac{32}{24 - x}) = \\frac{32 + 24 + x}{24 + x})
\\frac{32}{24 - x}) = \\frac{56 + x}{24 + x})
Cross multiply and solve for x
32 (24 + x) = (24 – x)(56 + x)
32 × 24 + 32x = 24 × 56 + 24x - 56x - x2
32 × 24 + 32x = 56 × 24 – 32x - x2
x2 + 64x + 24 (32 - 56) = 0
x2 + 64x - 24 × 24 = 0
x2 + 72x – 8x – 576 = 0
{x + 72) (x - 8) = 0
x = - 72 or x = 8
Speed of stream cannot be negative.
So, speed of stream = 8 km/hr