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20 Nov 2025, 23:42
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Let t be the time required for the downstream journey.
Set up two speed-distance-time equations (one for each part of the journey) as follows:
Downstream speed = v+3 = 90/t
Upstream speed = v-3 = 90/(t+0.5)
We have two variables and two equations. Solve them as a pair of simultaneous equations.
Combine them in a way that helps us to eliminate v and get a value for t.
Subtract the second equation from the first.
This gives us
(v+3) - (v-3) = 90/t - 90/(t+0.5)
6 = 90/t - 90/(t+0.5)
Divide both sides by 90:
1/15 = 1/t - 1/(t+0.5)
This will result in a quadratic equation.
To avoid doing the math, try plugging in answer choices.
Start with the middle one, option C, where t = 2.3.
1/15 = 1/2.3 - 1/2.8
It’s quite clear just by looking at the numbers that this will not work.
Similarly, just by looking at the numbers in the other answer choices, we can see that neither will options B, D, and E.
The only one that will work is option A.
Set up two speed-distance-time equations (one for each part of the journey) as follows:
Downstream speed = v+3 = 90/t
Upstream speed = v-3 = 90/(t+0.5)
We have two variables and two equations. Solve them as a pair of simultaneous equations.
Combine them in a way that helps us to eliminate v and get a value for t.
Subtract the second equation from the first.
This gives us
(v+3) - (v-3) = 90/t - 90/(t+0.5)
6 = 90/t - 90/(t+0.5)
Divide both sides by 90:
1/15 = 1/t - 1/(t+0.5)
This will result in a quadratic equation.
To avoid doing the math, try plugging in answer choices.
Start with the middle one, option C, where t = 2.3.
1/15 = 1/2.3 - 1/2.8
It’s quite clear just by looking at the numbers that this will not work.
Similarly, just by looking at the numbers in the other answer choices, we can see that neither will options B, D, and E.
The only one that will work is option A.
11 Apr 2026, 19:40
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I ended up framing the equation by including river`s speed as r in it, only to realize that this wasn`t needed at all.
I wasted a lot of time with that dirty equation.
Can someone please tell me why isn`t the speed of river not considered ? Or is there something to be told for that like running water or still water ?
I wasted a lot of time with that dirty equation.
Can someone please tell me why isn`t the speed of river not considered ? Or is there something to be told for that like running water or still water ?
12 Apr 2026, 00:21
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anushree01
You do not need the river’s speed separately because its effect is already built into the two actual speeds, v - 3 upstream and v + 3 downstream.
12 Apr 2026, 01:58
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Those who want to perform root of 1089 or any root in general faster. You need to apply the shrinking principle. Choose a range and slowly shrink as you go along.
root(1089) has to be between 30 and 40 and they give values from 900 to 1600.
Last digit is 9 thus it is either 33 or 37 only.
1089 is closer to 900 and 1600 thus we nee a value closer to 30 than closer to 40.
33 is closer to 40 and 37 is closer to 40. Or 37 would give a result that is more than half way towards 1600 or values above the mean of 900 and 1600.
Thus 33 is the root of 1089.
root(1089) has to be between 30 and 40 and they give values from 900 to 1600.
Last digit is 9 thus it is either 33 or 37 only.
1089 is closer to 900 and 1600 thus we nee a value closer to 30 than closer to 40.
33 is closer to 40 and 37 is closer to 40. Or 37 would give a result that is more than half way towards 1600 or values above the mean of 900 and 1600.
Thus 33 is the root of 1089.
DSGB
