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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. If the total distance
travelled is 90 km, x

User IHulk
by
3.6k points

1 Answer

12 votes

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,


Speed=(Distance)/(Time)


Speed* Time=Distance

A man walks for x hours at a speed of (x + 1) km/h, so walking distance is


D_1=(x+1)(x) km

The man cycles for (x - 1) hours at a speed of (2x + 5) km/h, so the cycling distance is


D_2=(2x+5)(x-1) km

Now,

Total distance = 90 km


D_1+D_2=90


(x+1)x+(2x+5)(x-1)=90


x^2+x+2x^2-2x+5x-5-90=0


3x^2+4x-95=0


3x^2+19x-15x-95=0


x(3x+19)-5(3x+19)=0


(3x+19)(x-5)=0


3x+19=0\text{ and }x-5=0


x=(-19)/(3)\text{ and }x=5

Time cannot be negative. So, the only possible value of x is 5.

User Rick Wayne
by
4.1k points