David knew he made a mistake when he calculated that Gilda walks 123 miles to the station. Read through David's calculations: Using d = rt, the distance is the same, but the rate and time are different. If Gilda misses the train, it means the time t needs 7 more minutes at a rate of 3 mph, so d = 3(t + 7). If she gets to the station 5 minutes early it means the time t can be 5 minutes less at a rate of 4 mph so d = 4(t - 5).
3(t + 7) = 4(t - 5)
3t + 21 = 4t - 20
t = 41
d = rt, so d = 3(41) = 123
Find David's mistake in his calculations. In two or more complete sentences, explain his mistake. Include the correct calculations and solutions in your answer.