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2 men at same tym start walking towards each other from A n
B 72 kms apart. sp of A is 4kmph.Sp of B is 2 kmph in 1st
hr,2.5 in 2nd, 3 in rd. n so on…when will they meet i in 7
hrs ii at 35 kms from A iii in 10 hrs iv midway
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Answer Posted / deepak
After the first hour, they are
4+2=6 km closer to each other. After the second hour, they are
4+2.5=6.5 km closer to each other, and so on. The reduction of distance per hour is therefore an arithmetic progression:
6, 6.5, 7, ...
with initial value a=6 and common difference d=0.5.
The arithmetic series (adding these distances) can be expressed in terms of hours, h, as
S(h) = ah + dh(h-1)/2
= 6h + 0.5(h^2-h)/2
= 6h + (h^2-h)/4
and they meet when this sum equals 72:
6h + (h^2-h)/4 = 72
24h + h^2 - h = 288
h^2 + 23h - 288 = 0
(h - 9) (h + 32) = 0
We have no interest in a negative solution, so the positive one h=9 is the one we want. They meet after 9 hours.
That doesn't match either of the answers that are times, so let's check the distance from A, which at a steady 4 km/h is clearly 36km, half the total distance.
They meet midway (answer iv).
| Is This Answer Correct ? | 7 Yes | 4 No |
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