Respuesta :
Given:
A man walks for x hours at a speed of (x + 1) km/h and cycles for (x - 1) hours at a speed of (2x + 5) km/h.
Total distance travelled is 90 km.
To find:
The value of x.
Solution:
We know that,
[tex]Speed=\dfrac{Distance}{Time}[/tex]
[tex]Speed\times Time=Distance[/tex]
A man walks for x hours at a speed of (x + 1) km/h, so walking distance is
[tex]D_1=(x+1)(x)[/tex] km
The man cycles for (x - 1) hours at a speed of (2x + 5) km/h, so the cycling distance is
[tex]D_2=(2x+5)(x-1)[/tex] km
Now,
Total distance = 90 km
[tex]D_1+D_2=90[/tex]
[tex](x+1)x+(2x+5)(x-1)=90[/tex]
[tex]x^2+x+2x^2-2x+5x-5-90=0[/tex]
[tex]3x^2+4x-95=0[/tex]
[tex]3x^2+19x-15x-95=0[/tex]
[tex]x(3x+19)-5(3x+19)=0[/tex]
[tex](3x+19)(x-5)=0[/tex]
[tex]3x+19=0\text{ and }x-5=0[/tex]
[tex]x=\dfrac{-19}{3}\text{ and }x=5[/tex]
Time cannot be negative. So, the only possible value of x is 5.
