Question

A group of tourists were supposed to cover an 18 km distance in a certain amount of time. However, they actually traveled at a speed which was .5 km/hour greater than what they had actually planned and thus arrived a half an hour early. What speed had the tourists planned to go at?

Answer 1

Answer: The speed that they planed to go, was 4 km/h.

Step-by-step explanation:

Let tourists planned to go at the speed of x km/h,

After increasing the speed by 0.5 km/h,

Their new speed = ( x + 0.5 ) km/h,

Total distance = 18 km,

According to the question,

The time taken at the speed of x - time taken at the speed of (x+0.5) = 1/2 hours,

$\implies \frac{18}{x}-\frac{18}{x+0.5}=\frac{1}{2}$

( Because, Time = distance / speed ),

$\frac{18(x+0.5)-18x}{x^2+0.5x}=\frac{1}{2}$

$\frac{9}{x^2+0.5x}=\frac{1}{2}$

$18 = x^2+0.5x$

$180 = 10x^2 + 5x$

$10x^2+5x-180=0$

$5x^2+x-36=0$

$2x^2 + 9x - 8x - 36 = 0$

$x(2x + 9) - 4(2x + 9) = 0$

$(x - 4)(2x + 9) = 0$

⇒ x - 4 = 0 or 2x + 9 = 0  

x = 4 or 2x = -9  

x = 4 or x = -9/2 = -4.5 (not possible)

Thus, the speed that they planed to go = x km/h = 4 km/h

Answer 2

The answer is 4 km/h. if you need more exlaination just let me know :)