Enter an equation that can be used to solve this problem, where x represents the number of hours that Roberto had been traveling.
Roberto left his parent's house at 11 A.M. traveling at an average rate of 30 mph. His parents left their house at 12 P.M. traveling at an average rate of 45 mph going the same way as Roberto so that they could catch up to him. After how many hours will it take Roberto's parents to catch up to him?
Enter the amount of hours after Roberto left that it will take Roberto's parents to catch up to him (assume that they do not stop).
Equation:
h:
+37084 Roberto's distance at time 't' = 30 + 30 t (the 30 is the headstart he got by going one hour earlier)
His parents distance is 45 t
When are they equal?
30 + 30t = 45t
30 = 15t
t = 2 hours after 12 o'clock Roberto traveled 90 miles, his parents traveled 90 miles (this will be 3 hours after Roberto leaves.....and only two hours after his parents leave)
+129840 Let T be the time [in hours] for Roberto to travel.......and let {T - 1] be the time for his parents to travel......and since theyboth travel the same distance when his parents catch up, we have
Roberto's Rate * His Travel Time = Parent's Rate * Their Travel Time
30 * T = 45 * [ T - 1] simplify
30T = 45T - 45 add 45 to both sides, subtract 30T from both sides
45 = 15T divide both sides by 15
3 = T → it will take his parents [T - 1] = [3 - 1] = 2 hours to catch him
