a man travels 108 km and find he could have made the journey 7/2hours less ,had he travelled 2km an hour faster ;at what rate did he travel
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A man Travels 108 km and find he could have made the journey in 9 by 2 hours Less, had travelled 2 km an hour faster at what rate did he travel
Ask for details Follow Report by Madhusahni 02.06.2018
Answers
pravinsir
pravinsir Ace
Let the man travels with speed x km/hr
so time taken to cover the distance of 108 km ,
= 108 / x
if speed increases by 2 km/hr
i.e. now speed = x+2
then time requires to cover 108 km ,
= 108/ x+2
these two time has difference of 9/2 hour
therefore , 108/x - 108/x+2 =9/2
[108(x+2) -108x ] / x(x+2) = 9/2
108x + 216 -108x / x^2+2x = 9/2
216 / x^2+2x = 9/2
9 ( x^2+2x ) = 216 ×2
9 x^2 + 18x = 432
9 x^2 + 18x - 432 = 0
x^2 + 2x - 48 = 0
x^2 + 8x -6x - 48 = 0
x ( x + 8) - 6 ( x + 8) = 0
(x + 8 ) (x - 6 ) =0
(x + 8 ) = 0 or (x - 6 ) =0
x = -8 or x = 6
speed never minus
therefore x = -8 not possible
so , x =6
Answer:
x km/hr
so time taken to cover the distance of 108 km ,
= 108 / x
if speed increases by 2 km/hr
i.e. now speed = x+2
then time requires to cover 108 km ,
= 108/ x+2
these two time has difference of 9/2 hour
therefore , 108/x - 108/x+2 =9/2
[108(x+2) -108x ] / x(x+2) = 9/2
108x + 216 -108x / x^2+2x = 9/2
216 / x^2+2x = 9/2
9 ( x^2+2x ) = 216 ×2
9 x^2 + 18x = 432
9 x^2 + 18x - 432 = 0
x^2 + 2x - 48 = 0
x^2 + 8x -6x - 48 = 0
x ( x + 8) - 6 ( x + 8) = 0
(x + 8 ) (x - 6 ) =0
(x + 8 ) = 0 or (x - 6 ) =0
x = -8 or x = 6
speed never minus
therefore x = -8 not possible
so , x =6
Step-by-step explanation: