A train travels at a constant speed of 24 24 miles per hour. Which equation and table show the correct relationship between h h, the number of hours, and d d, the distance traveled?

Solution:

Distance $=54 /; km$

Let the average speed be x

Distance = 63 km

The average speed to cover this distance $=x+6$

Total time taken $=3 hr$

$/large/frac{D}{S}$$=t$

$/therefore / large/frac{54}{x} + / frac{63}{x+6}$$=3$

$/large/frac{54 (x+6) + 63 x}{x (x+6) }$$=3$

$54 x+324 + 63x = 3x^2 + 18x$

=> $3x^2 - 99x - 324 = 0$

=> $x^2-33 x-108 = 0$

$ (x-36) (x+3) = 0$

$x=36 /; or - 3$

$x=-3$ is not admissible

Hence $x = 36 km/hr $ is the speed