Help Please?.............................A man started on a walk of 12 km?

Question

A msn started on a walk of 12km. After walking half the distance at x km/h, he decreased his speed by 1/2 km/h. He completed his walk 10 minutes later than he would have done if he had not decreased his speed.

(Obtain an equation for x and solve it. Use your value of x to deternine the time he took for the 12-km walk. ANS x 4 1/2, 2h50min)

Answer 1

starts with x km/h

distance 'd' to cover = 12 km

speed after 6 km = x- 0.5

Time it would take to cover 12 km at x km/h = 12/x

time it would take to cover as it is presented in the scenario = 6/x + 6/(x-0.5)

also it is give that the second time is 10 minutes longer than the first time.

10 minutes is 1/6 of an hour

Therefore:

{6/x + 6/(x-0.5)}-{12/x} = 1/6

{6x-3+6x-12x+6}/{(x)(x-0.5)} = 1/6

18 = x^2 - 0.5x

Solve for x and get x = 4.5 km/h

So he started walking out at 4.5 km/h

time taken to complete 12 km = (6/4.5 + 6/4 ) x 60 minutes = 170 minutes = 2 hour 50 minutes

Answer 2

6/x + 6/(x - 1 km/2 hr) = 1 hr/6 +12/x
6(x - 1/2) + 6x= x(x - 1/2)/6 + 12(x - 1/2)
6x - 3 + 6x = (x^2 - x/2)/6 + 12x - 6
- 3 = (x^2 - x/2)/6 - 6
- 18 = x^2 - x/2 - 36
2x^2 - x - 36 = 0
x = (1 ±√(1 + 288))/4
x = (1 ±√289)/4
x = (1 + 17)/4, (The negative root is discarded)
x = 4.5 km/hr
t = 12/4.5 hr + 10 min
t = 2 hr 50 min
t = 6/4.5 + 6/4
t = (24 + 27)/18 = 51/18 = 54/18 - 3/18 = 3 - 1/6 hr
t = 2 hr 50 min

Answer 3

d= v*t so t = d /v

Total time taken at constant speed of X km/h = 12 / X hrs

Variable speed walk:

Time for first 6km = 6 / X hrs

Time for last 6km = 6 / (X-0.5)

Total time for variable speed walk is:

6/X + 6/(X-0.5) = 6[1/X + 1/(X-0.5)]

= 6*(2X-0.5) / (X*(X-0.5))

10 min = 1/6 hr

You are given:

12/X = [6*(2X-0.5) / (X*(X-0.5))] - 1/6

multiply through by 6*X*(X-0.5) to get:

72(X-0.5)= 36(2X-0.5) - X*(X-0.5)

72X-36 = 72X-18 - X^2 + 0.5X

X^2 -0.5X-18 =0

From quadratic formula:

X = (0.5+sqrt(0.25+72))/2 = 9/2 = 4.5 km/h

The time for his walk is:

6/4.5 + 6/4 = 17/6 = 2 5/6 hr = 2hr 50min