Question

A boat travels downstream from point a to b and comes back point c half distance between a and b in 18hours if speed of boat is still water 7km/h and distance ab=80km then find the downstream speed

Answer 1

Answer:

10km/hr .....MB

Step-by-step explanation:

distance travelled from B to C

= 80/2 = 40 km

S boat = 7km/h & let speed of stream= x

S down = 7 + x

80/(7+x) + 40/(7 - x) = 18

on solving this we will get x = 3

speed downstream

= 7 + x = 7 + 3 = 10 km/hr

Answer 2

Downstream speed is 10 km/hr

Solution:

Given that,

A boat travels downstream from point a to b and comes back point c half distance between a and b in 18 hours

Distance AB = 80 km

Therefore,

Distance to point c = $\frac{80}{2}$ = 40 km

Speed of boat is still water 7 km/h

Time taken = 18 hours

Let the speed of stream be "x"

From given,

$\frac{\text{distance between a and b }}{speed\ downstream}} + \frac{distance\ to\ point\ c}{speed\ upstream} = 18\\\\\frac{80}{7+x} + \frac{40}{7-x} = 18\\\\80(7-x) + 40(7+x) = 18(49-x^2)\\\\560-80x + 280 + 40x = 882-18x^2\\\\840 - 40x = 882 - 18x^2\\\\18x^2 -40x -42=0\\\\9x^2 - 20x -21 = 0\\\\Solve\ for\ x\ using\ quadratic\\\\x = 3\ and x = -0.777\\\\Ignore\ negative\ value\\\\x = 3$

Thus speed of stream is 3 km/hr

Downstream speed = speed of boat in still water + speed of stream

Downstream speed = 7 + 3 = 10

Thus downstream speed is 10 km/hr

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