your aunt was visiting your home, and 5 minutes after she left you realize she forgot her purse. you leave right away and drive to catch up with her. your average speed is 10mi/hr faster than her average speed and you catch up to her after you have been driving for 20 minutes. how fast did you drive
We know that the distances were equal so lets set the two equations equal to each other. Distance = Rate * Time
Aunt's rate * her time = Your rate * your time
Let R = your rate
(R-10)(25/60) = R(20/60)
(R-10)(0.4167) = R(0.3333)
0.4167R - 4.167 = 0.333R
0.083367R / 0.083367 = 4.167 /0.083367
R = 50 mph
check:
Aunt's rate * her time = Your rate * your time
40mph* 25/60 = 50 * 20/60
16.667= 16.667